Yes it is, I agree, in theory the UK has always had 'control' over immigration (every government has), even within the EU, but successive governments of every hue have failed to implement or use the levels/levers of control that are required to exercise anything like effective control. This was either because it cost too much; or it would at times to have worked effectively have had to be fairly brutal in its application and 'humanitarian' considerations, especially in an espoused 'Liberal democracy' would not allow such brutality; or until relative recently because it seemed the majority of the populace didn't care too much, one way or the other and the UK had built something of a reputation of being ready to help out with emergency asylum situations, e.g. when East Asians were forcibly removed from Kenya, etc.
However, it is assumed the main reason that successive governments did not implement stricter overall immigration controls was it was all too much trouble and asylum seekers only really popped up now and again in large swathes, although it was known others, not the true asylum seekers, but those just desperate to get in, did find their way in although mainly illegally.
Then of course the 'freedom of movement' in the EU set off a 'number of hares' running, that such as Farage moved in on, almost immediately.
None of the EU citizens (as far as I am aware) ever came to the UK to seek asylum, but it all got lumped together, including loss of jobs and over stretched hospitals and shortage of housing, etc.Anyone watching us from a distance would have seen Brexit coming, but David Cameron, buoyed by first his Election victory(after the coalition) and a couple of years later seeing off a strong Nationalist challenge in INDY1, in Scotland that also decimated (and then obliterated) Labour in Scotland, he decided to go for the hat-trick and put his Conservative 'anti EU brigade' to the sword once and for all and he issued the sloppiest attempt at a operating a fundamental referendum that one could have expected.... one he was oh so confident of winning. The rest as they say is history.
As a result, months, years and more yet still to come will follow of chaos over immigration/asylum etc. with the true picture getting blurred over and over again, because after twelve years of power the Tory's now know their only hope of a) winning and/or b) avoiding a drubbing at the next Election, is to 'go big' on immigration (well actually asylum seekers, really).