Food and drink in the supermarket has not gone up by 10-20% since the vote, that is complete rubbish.
The whole tariff / quota situation is currently hear say, nothing is concrete to what will happen. The UK import quite a lot from Europe, I can't see why the EU would hinder one of its biggest customers by increasing prices through tariffs as the UK will just go elsewhere. At the moment this is just a stance the EU is putting up to ensure they receive the 'divorce payment'.
Again with the banks, I know of some banks that have opened new branches in EU countries but as yet they have not confirmed moving their main headquarters to the EU from the UK. If this was to happen the UK are bound to offer incentives to stay, as they are already doing with lower corporation tax.