Well, I very much doubt that there are any foreign nationalities working in the police. I'm pretty sure you have to be a British citizen to join the constabulary. As Sat TV says, those non-white faces you see are the offspring of immigrants, often going back a few generations, and I think they'd be quite annoyed to be referred to as foreign. However, yes, you're right we do have a long colourful history of immigration into Britain, to the extent that we're all mongrels more or less, though a member of the British National Party would no doubt give me a kick in the head for daring to say such a thing.
The problem here is that we're talking about different things. There's governmental policies regarding immigration and addressing racism, there's the man on the street's attitude to foreigners, and there are differing attitudes to white and non-white foreigners. Britain does have an immigration policy but that's because it really needs one. As a rich country with lots of free social care people do flock here, it's true. If there's a greater percentage of immigrants in Britain than in Taiwan (and to be honest I have no idea), it will be because there are lots people trying to get in and stay. However, the other reason that there's an immigration policy is because governments are scrutinised upon them come election time. And the reason for that is because so many people either just plain hate immigrants or are simply feeling that our resources are better spent on native Brits (whatever that means).
The plot thickens further though because it's in fact only the non-white immigrants that anyone really cares about. Sure, if you go back 50-60 years it was the Jews, then the Irish, that were seen to be the problem but recent waves of immigration have been brown or black so now everyone's focused on them instead. It's hard to generalise, but large parts of British society are deeply racist, mainly the older generation and some sectors of the working classes. We've had race riots in the not too distant past. As an ESOL teacher I have known many, many immigrants over the years and they do not get an easy ride by any means. We are far from a welcoming society unless you happen to be white (not including Americans, who are generally thought of as a bit thick and quite annoying Seriously, though, an American ESOL tutor of mine had some negative experiences with other parents at her children's school. Or Polish too, come to think of it. Lots of bad feeling about Polish workers taking our jobs)
In the public services the percentages of non-whites recruited do not reflect those in the population which can lead one to conclude there's institutional racism operating there. The cost of applying for indefinite leave to remain or British citizenship is huge now, about £900 I think (45000 NTD) and if your application is incomplete they give you a few days to get the evidence to them before turning down the application with no refund. You also have to pass a test that 99% of Brits would not be able to pass themselves without study.
I could go on. In fact, I will. My son was recently attacked on a bus because his girlfriend is Chinese. I must ask her the next time I see her whether she has anyone assuming she can't read English and insisting on giving her a menu in Mandarin when she eats out. And if she's upset when it happens over and over again.
Having said all that, Britain is still probably a better place to be foreign than Germany or France. The last I heard of Germany there were gangs of neo-Nazi skinheads targeting the Turkish communities. And in France they've banned the burkha.