TB, your sentiments echo mine.
Brits (particularly those of the older generation sitting in old colonial buildings in ex-dependencies, as Shri identified) love thinking their culture is unimpeachable, that we have nothing in common with any other Europeans etc, but the reality is that when you walk around London, the city has benefitted enormously from the influx of migrants (european or otherwise). All the different faces and voices are what makes London such an economically, culturally and artistically rich place.
Shri also made the point that we've all benefitted from economic migration, so there's a bit of hypocrisy from those claiming to close borders, for their dear country to be more nationalistic (or xenophobic, for what of a better word), all the while being in a country and benefitting economically from shortages in the job market which locals here could not fill.
I know of loads of expats here who have mixed-race, mixed-nationality kids. How does their view to close the UK's borders balance with the possible inability of their children to go back? If a country is led down the path that the exiters would like, there would be real problems I think. There are already significant economic hurdles for Brits who have married non-Europeans to get back home (and these hurdles are 100% British, nothing to do with the big bad EU). I wonder whether those pro-exit expats kids be proud of their dads? When you break down the arguments in granular detail, it's all just hypocritical, double standard, bullshit noise.