The type of immigrants which integrate well in the UK are the same ones which integrate just as well in Greece (mostly christian-derived ethnicities). The Muslim population on the whole has not integrated well in the UK nor anywhere else - including Cyprus and Greece. The British are only now admitting their problem with immigrants as austerity measures bring the country down to the poverty levels experienced by Greeks over the decades (not just recently).
From the recent UK census it was found that over 4% of UK residents could NOT even speak English and some 3 million lived in households where no adults speak English as their main language.
I also know from experience that Greeks/Cypriots are merely more honest in voicing their contempt of unattractive differences in foreigners (not the same as racism) whereas most British people are too afraid to voice their prejudices for guilt over their Empire-days atrocities.