I think you touched on some important issues about the lack of integration between different cultures, this is a problem in our society. Having said that, in my experience there is a rather large racist crowd in this country. I think you only need to speak to many people, particularly your average blue-collar working man or woman to see that they do have something against particular ethnic groups. These people are not the exception. Yhorian, if you cannot be bothered to read this whole post (and I wouldn't blame you) read the last paragraph.
I understand both sides of the issue. If you, or any one of us for that matter, were to go live in Saudi Arabia for example, we would not go find an Arab village off in the sticks in bumblef*ck nowhere to live. We would live in and integrate into a Western community. Disregarding the fact that we would probably get beaten senseless in an Arab village for being part of the 'Evil Western Empire', we would not live there because we wouldn't be familiar with the language, culture, religion (in most cases) , plus our surroundings would be very alien. It is natural to want to live somewhere you feel safe and secure and accepted. Applying this logic to immigrants, it is no surprise they form their own niche within our society when they move here. It is an unfortunate situational side effect that living in these communities often excludes them from our society.
Also, imagine you are from a conservative Muslim family and you move into inner city London, Birmingham, Nottingham or to even some extent, Cardiff or Swansea. You will be assaulted by things you are protected from in the Middle-East, Pakistan etc such as the clubbing culture. To Muslim parents when they come to this country and drive down the Kingsway or Wind Street (You must know the Kingsway or Wind Street living in Cardiff, the two main watering holes in Swansea. I use this as example since I am from there and have been clubbing there many a time) you will see people fighting, staggering around, throwing up and if you are unlucky enough, having sex down back alleys. Their cities by comparison are tame. There is still alcoholism, clubbing, drinking and so on but it is all done behind closed doors. It's not up front and in your face. To them these things pretty much Herald the apocalypse. Due to this and various other cultural clashes you find the first generation immigrants will not even attempt to integrate. In many cases the second or third generation immigrants will.
To further compound matters the Government actually subsidizes immigration into this country. People claim asylum or cheat the system and are paid to do so. This actually allows your first generation immigrant with 4-8 kids to stay reasonably self-sufficient and not be forced into a situation where he needs to integrate with our society. I suppose the upside to our system is that people without the necessary linguistic knowledge to communicate with us, and there are many who cannot do so, are not driven to crime or incredibly drastic measures to survive. Look at your average labourer though - John Smith living in St. Helens (a predominantly Asian part of Swansea) who grafts for a living and pays his taxes, is watching Mohammed down the road claim benefits when he was not even born in the country. John only earns marginally more than Mohammed working hard manual labour while Mohammed gets subsidized by our Government. John's taxes (which is about 22p to every £1 if he is in the lowest tax bracket. 22% of his earnings - higher if he goes into a higher tax bracket.) go in part to fund Mohammed's lifestyle. Mohammed is getting hand-outs from the state and is managing in supporting his 6 kids, while John can barely afford to support 2. John starts to resent the Arab who cannot speak a word of English and gets to talking with his friends in the local Pub. They all feel the same. Meanwhile Mohammed is watching John stagger home drunk past his house at 11pm on a Friday night (his holy day.) Okay, aspects of this example may be slightly exaggerated, but you get the picture. Therein the problem lies.
I have not looked at many figures but the BNP* membership, I am sure, are comprised in majority by people like my fictional character. Honest, hard-working families mostly in cities and built up areas bordering ethnic communities (in particular, Muslim - but other communities also in some instances) who are pissed off with the Governments for giving hand-outs to immigrants too liberally. The only solution is, that the Government is FAR more selective about who it allows into our country because if they drop the financial aid that they give to immigrants poverty driven crime will increase and you will end up with ghettos in worse states than many areas are now economically.
So to get back to your point Yhorian. If people were saying, 'I hate Mohammed over there, he's taking money from our Government that I pay with my own taxes.' Fine. Not racist at all. They are citing one person, an individual. But people don't say that, at least not many of the large number of people that I speak to in Pubs, in my family, on trains, people that I read about in news. They say 'I hate those Muslims, they don't integrate. They take my taxes. Blah Blah Blah Blah.' or another classic 'Now I have nothing against THEM and i wish THEM no harm but in all seriousness they can get the f*ck out of our country and go back to Mecca.' There is racism in this country and no matter what guise it falls under when certain members of my family (who shall go unnamed but fall under the above category of working people etc etc) are talking over Christmas dinner about the BNP and how the (race) war is coming and all the people in their office are doing the same i think it is fair to say there is racism in this country. I'm not sure who you deem a 'classic' racist but if you are talking about BNP political leaders or skinheads, to be frank, they do exist. The BNP is a political party so whatever their leadership says (obviously) is closely scrutinized. It doesn't mean their not racist if they preach a not-so-extreme right wing view (if there is such a thing) in public and then are saying different things in private. As far as I'm concerned they would have fit right in in 1940s Germany screaming 'Alle Juden raus!' The only difference is, the demographic they discriminate against and the fact that our present society as a whole would never, ever let something like that happen again.
*For the Americans who don't know, the BNP is the 'British National Party', a right wing political organization which is fairly well known in this country.