A couple of points:
the situation with lots of immigrants coming in is in no way unique to the UK; there is a similar situation in most of Europe (not to mention all the refuges in parts of Africa and Asia)
it is very unlikely that those cultures will end up totally swamped; dominant cultures tend to have a great capacity for assimilating newcomers- look at 19th century US for instance
in other countries, a fair proportion of these immigrants are English- they have to put up with you (and don't imagine that English ex-pats are unusually good about adopting local customs)
English is also the lingua franca used between different groups of immigrants
it is therefore particularly unlikely that the English language and culture will be swamped
the fact that people use a foreign language when out with the family doing their Saturday shopping tells you nothing at all about their linguistic capacity
I teach at an English university, my scholarly papers are written in English and I work as a proof-reader of English academic texts- so I don't think I am exactly contributing to the erosion of the language
my children speak English at school and nobody thinks of them as anything but English
we do, however, reserve the right to conduct family conversations in any language that we please