Sorry for the late reply, but seriously?
The UK has what amounts to a unwritten constitution, hence the two 'big dog' political parties fighting it out for power, is the only thing that has a chance of working.
Bullshit. Evidence please that no other democracy has more than two parties and a functional society and government.
Please explain why the Dutch government consisting of 4 parties right now (VVD ((neocon) liberals), D66 (liberal democratic republicans), CU (Christian Union) and CDA (Christian Democratic Alliance), is not just more stable than your government, but can also implement more policies and even quite reformative policies, if your statement is correct that only two major parties can vie for power without having a chance of working. (Let alone your later claim of significant achievement).
Fact is, we've got alliances of chunks of parties who all have to compromise, meaning only the most pragmatic and realistic solutions have a chance of getting through. Pure ideological solutions (those that consist of radical ideological reform and revolutionary ideas) are on the backburner or are being deconstructed to take the best and most agreeable parts that work in everyone's interest get through.
In your case, you've been going between extremes of Thatcherite economies and Labour economies and have been running on a pure neocon agenda for a decade now. And to be honest, it created mess after mess after mess and a hugely disenfranchised, demoralised, apathic and antagonistic public.
If anything, your system shows how ludicrous giving too much power to onesided policy makers is.
The 'Will of the People' etc has nothing to do with it,
Of course it has everything to do with it. The Will of The People cannot be represented in a binary system, let alone by a single party. At all. Any party, let alone any politician that claims to be implementing the Will of the People (their agenda of course) is fundamentally untrustworthy and should be treated with incredible scepticism. They're by default charlatans and frauds, because no single policy can captivate the ideas of millions of people.
as demonstrated by the failure to implement the referendum result.
The problem with implementation is that nobody knew what the referendum result meant. "Brexit means some sort of leaving the EU, we'll figure it out as we go along" is an utterly ridiculous referendum design. The failure of the referendum implementation lay in its fundamentally flawed design by creating a deliberate vagueness and uncertainty.
The only clear answer, as in, what would it have meant, would have been remain, because it would have retained a predefined status quo. Even if your politicians have failed to communicate this in an incredibly poor showcasing of running the pros and cons against one another in any fair way whatsoever. Probably because they've been using the EU as a scapegoat and lightning rod for any anger towards the failures of their own domestic policies. Which normally in a binary political system would have been directed at the party in charge. In a system with more parties, like ours, it means the government coalition is refreshed and politicians are encouraged to work to improve their policies and keep them in line with public interests. In your system, it will swing the other way around by default and there's no incentive to change and improve, because you just have to wait for the failure and subsequent implosion of your only opposition.
That said, you had on the Leave side Farage advocating a Norway model, a Suiss model, an Icelandic model, a Canada model and ultimately he's now going after "no model at all" and Johnson followed suit because the Americans want that for their trade deal. I'm sorry to break it to you, but this mess is entirely, 100% the fault of the Tory leadership and Leave campaigners fraudulent and vague campaigning. They're too incompetent to lead and get consensus within their own party of just a few hundred MPs, let alone a nation with millions of people, each with their own interpretation.
They failed to communicate what they would go for, mostly because they had no idea themselves what they were campaigning for and made loads of really dumb assumptions on how the EU would roll over for them without even having a fundamental understanding of what the EU entails.
Politicians in the UK do not want to know the 'will of the people', they tell the people what their will is. This is how the principle of an unwritten constitution works out by using precedence. If you are the only ones who have set precedence, since the days of King John and the MC, then you won't give that up.
This too is incorrect. King John ultimately had to share power with the Anglo-Saxon nobility. I cannot recall Labour being part of said nobility.
The principle of an unwritten constitution is that it can be changed by parliament if there's sufficient demand for change within society. The goal of an unwritten constitution is to be amended to the times. Precedence has been set by parties other than the elite, the problem you're refering to is the concept of holding absolute power and therefore not having to take into account the will of other people and therefore the unwillingness to share power with coalition partners or opposition.
This has nothing to do with the unwritten constitution and how it can function, it has everything to do with greed, self-righteousness and self-centredness, on top of the idea of efficiency is only possible in a homogeneous design environment. Some of the lesser aspects of human nature. In practice however, a multifacetted design approach can create a more optimal result, even if it costs more deliberation and therefore more time in the establishment of what it is you want. So yes, a coalition may take more time to form, but the result is a multipronged approach to tackling problems with a wider support and more aspects taken into account than those of interest to a homogeneous group.
As an engineer and designer myself I've seen many solutions from homogeneous design environments, which usualy show insufficient thought being put into certain aspects of the design.
Consider the image below and try to imagine each group to be a political party.
Now compare that to:
Now think of what an aircraft would look like if only one group would be in control, or a design that is influenced by just two groups. It will be fundamentally flawed. It'd be like having a football team consist solely of goal keepers. It's never going to win. Combining defenders, midfielders, goalie and forwards in a certain way where each group has their interests covered and complemented by the other groups results in a team victory: everyone gains.
Almost all battles political or otherwise only really have a successful outcome when there are only two opposing sides, one wins the other loses and of course history is always written by the winners.
Define "succesful". It sounds like you mean "succesfully implemented one's entire own program" (to the detriment of everyone else). It's a very narrowminded definition and I can't disagree more.
Political battles are battles when they're designed around a winner takes all. There is such a thing as political cooperation. In the Netherlands we had a situation at one point in our history where literally battling factions cooperated in the water household of the land in between with mutually agreed policies (compromises), because it would be in both parties' interest to achieve something positive. You think in black and white outcomes. There can actually be such a thing as both groups having similar and overlapping interests, thus succesful could simply mean having a productive outcome.
From the above I'm slightly convinced you think transactional about treaties as well. As in, there's going to be a winner and loser in any confrontation. A very Trumpian (shortsighted egocentric) way of looking at things. What if treaties can be beneficial to both sides? Take for instance treaties regarding access to the Suez or Panama canals. Think of the Geneva Convention regarding the practices of war and treatment of prisoners of war. Think of trade agreements where hurdles are removed for both sides.
Hell, even in football two sides can benefit over a third party from a draw.
Also, you know that World War II thing? Where an ALLIANCE of nations beat another alliance of nations? You think that would have been possible if just the interests of a single nation had been at stake? Do you not agree that each of those participating nations on both sides involved didn't have their own priorities? And you know what happened? The side which ultimately had only the interests of a single political party in mind, with full control by a single person even and with the strictest hierarchy involved... LOST. Decisively.
Why? Because going it alone makes one weaker. Divide and Conquer is an often employed strategy for good reason.
Three (or more) way battles occur when not everyone can be contained in the big tents of the opposing parties, this leads to mistakes, or to unintended consequences, e.g. vote for one thing and get another. It confuses friend and foe alike and quite often leads to nothing of any significance being achieved, especially when bold actions are required.
Lot to disagree with here, I'll try to cover it pointwise.
1. You can't contain everyone (of the opposition or otherwise) in the big tents. First of all, a big tent suggests a compromise. Yet if one of these big tents is ideological, like Labour or the Tories, this usualy means you're forced to vote for "at least they're not the worse option for me" (ie. current government party). It gives no incentive to these parties to take your views into account, exactly because they know you have no alternatives. Big tents lead to a narrowing of the people being catered to by default and allows for massive, unpenalized disenfranchising, as long as you're not worse to them than your only big rival.
2. By creating two big tents you're automatically disenfranchising people of diverging views and thereby guarantee losers, disgruntlement and apathy and a lack of say and influence, let alone control.
3. When you have but one or two choices, you can't pick the best of each side on offer. Particularly not from parties that didn't make the cut. As a voter, you'll automatically lose on some policies even if you won on others.
4. Mistakes and unintended consequenties are guaranteed because the people involved are human. A single party in charge does not lead to fewer errors made. It leads to fewer corrections and ignoring of mistakes and unintended consequences being rebranded as 'features' and "intention".
Nice Brexit example: "We want to make everything economically better for the UK by leaving the EU" ----> "I will accept being poorer and economic setbacks for decades as long as we leave the EU and I'll even accept the breaking up of the UK". I mean, come on. FFS.
5. Having just a few parties also leads to more corruption, since the same people are in power for longer periods of time, thus the number of people to corrupt reduces.
6. Having a single party in charge does not mean you can achieve something of significance. It does not preclude it either, but it's no guarantee of anything. Especially if the party in question is either not ambitious, overambitious, incompetent, corrupt and/or delusional. By your definition North Korea should be the epitome of successtories. Please...