With regards to Europe, non-white populations were much smaller than in the US, making them less of a perceived threat. As Quirite already noted, the nearest comparison to segregation is probably the anti-semitic laws associated with Nazism.

Speaking specifically about the United Kingdom, I believe that during WW2 there were some tensions locals and US soldiers based in the country because of the latter's more strongly racist attitudes.

Something to note about the UK is that the British Empire, and later the United Kingdom and colonies had a "single united citizenship" that was not fully replaced until 1982. However until the 40s or 50s, the UK was mainly an exporter of people, with limited immigration from the Empire. The non-white population of the UK only really rose to a significant size in the 50s and 60s, with immigration coming first from the Caribbean, then Kenyan Asians in 1967 and Ugandan Asians in 1972. The 50s and 60s were largely periods of high employment and even labour shortages, which softened the social impact of immigration. So the UK was in a very different position to the US. Even now the population here is much more homogeneous than the US.

The first measure of segregation is where people live. Black immigrants "had to face persistent discrimination and they were often forced to find flats or houses ... in so-called 'zones of transition' within the great cities." Good examples of these areas are Notting Hill in London and St Pauls in Bristol (which I can look out over from my window here). This kind of segregation was not dominant in the 1950s or 60s though.

[T]here was little sense at the end of the 1950s that many of the minorities would either deliberately seek or be driven by circumstances to settle together in relatively segregated areas. Indeed, it could still be pointed out in 1958 that 'despite some concentrations' the minorities were 'dispersed throughout the country', and that the majority of English people hoped that there would be full 'assimilation'.

What we don't see in the UK is quite the same sort of legal or institutional segregation that took place in the US. Which is not to say that British institutions were (and are) not racist. It's only 15 years since the Metropolitan Police was found to the "institutionally racist." (Personally, I like this sketch from Not the Nine O'Clock News in the early 80s.) There's the (in)famous speech by the prominent politician Enoch Powell about immigration in which he compared himself to the Ancient Romans seeing "the river Tiber foaming with much blood." However these things go alongside serious efforts to improve race relations, with particular credit going to Roy Jenkins, a liberal Home Secretary. 1965 saw the introduction of the first Race Relations Act, aimed mainly at discrimination in housing.

Social relations also show a mixed pattern. To pick out two examples, 1958 saw race riots in Notting Hill and 1963 the 'Bristol Bus Boycott' over the bus company's refusal to employ black or asian crews.

In 1958, when an estimated 210,000 people from 'coloured minorities' were living in Britain, there were serious disturbances in Nottingham and Notting Hill, started not by black newcomers but by 'nigger hunting' youths, still vaguely known as 'teddy boys'. According to the judge who sentenced nine white youths after Notting Hill, 'it was you men who started the whole of this violence in Notting Hill. You are a minute and insignificant section of the population ... and you have filled the whole nation with horror, indignation and disgust."

(All quotes from A Social History of England by Asa Briggs.)

IANAH, but I would like to address your question nevertheless...

It is my understanding that such a thing was not common in Italy, except of course for a particular period under Fascism (1938 - 1944) during which the Racial Laws were enforced, mainly against those Italians of Jewish descent. These has also effects on the colonies, as the locals had up to that point enjoyed a relatively cordial relationship with the Italians (these were mainly the Somalians/Eritreans; Libyans and Abyssinians were understandably not so keen towards us). Suddenly they found themselves barred from entering cinemas, cafes, and the like... and sexual relations between the two groups became also a criminal offence.

After Mussolini's fall those laws were repealed but interestingly enough, the Allies kept enforcing them in the former Italian colonies now under their control until the end of the war.

Jewish ghettos have a really long history in Europe (since well before the rise of Nazism), and the Romani faced similar treatment historically. Latin America had a pretty awful caste system traditionally as well.

By the 1950s Europeans were rightly very critical of America's systematic segregation. WW2 really played a big role in showing them just how serious the US was about it.

Europe had its own racial issue though: Colonialism. Europe held onto many of its African colonies well into the '60s. That is a whole other issue, but I think it exposes a lot of the same human weakness that white Americans were exhibiting at the time.