There has been some momentum on wage rises now for about 18 months, I suspect its sitting above the people getting minimum wage but that's speculation. Its a hard barrier to break, move a job from minimum wage to paying above that, psychologically for companies.
There is no doubt the EU and the ability for labour to move to the UK will keep wages supressed as there is a ready supply of labour willing to work for the UK minimum wage. I bet there are literally millions who would be ready to hop on a plane/train to come to the UK to do a minimum wage job. The wages would look seriously high to a lot of them, they would probably be quite unaware of the cost of living here though hence why they tend to congregate together in largish houses with a room each.
I remember 15-20 years ago working with Aussies and New Zealanders, they came here as the comparative wages were higher, they did some Europe travel and earned more than comparative jobs down under. 3-4 years and they would mostly go home, with more in the bank than if they had stayed down under and having done quite thorough travel to Europe, saving shed loads than having to do a few long hauls later on. Even they tended to congregate in small groups to live, yes they certainly mixed far far better in daily life, going out etc but they did seem to find it easier to live together than go alone or move in with brit housemates.