Yeah, I don't think British culture is something the government should legislate to 'protect', especially if the suggestion is that 'protecting British culture' means deporting immigrants or other racist nonsense like that, but I think it's pretty ridiculous to suggest that there's no such thing as British culture.
I do recognise what the poster above says about breaking it down into Northern culture, West Country culture, Scottish culture, etc, but I think you could make that argument for any culture or nation.
Rural Anatolian culture is very different to that in liberal coastal cities like Izmir, but you can still say that there is such a thing as Turkish culture. Provencal culture is pretty different to culture in northern France, but again, I think there is an overarching sense of Frenchness.
Every country is full of contradictions and parts that can't easily be reconciled. And the nature of the United Kingdom also makes it pretty hard to disentangle Scottish, Welsh, etc culture. And if you insist that sub-UK phenomena can't be counted as British culture then I guess that makes it more complicated as well. eg. Can we count fish and chips as British culture or must we call it English? Is the love for the NHS a British trait or not (after all there is no NHS in NI)...?
For me British culture and life encompasses everything from curry and chips, to Doctor Who, sprinter trains rattling past five-a-side games on the local playing fields, the pips on Radio 4, a kebab on a rainy Friday night, Coronation Street, the Christmas copy of the Radio Times, an English breakfast in a greasy spoon, old counties with quaint names like Lancashire and Perthshire, red-brick terraces, ruined castles, Yorkshire Tea, cheddar cheese, the dulcet tones of David Attenborough, silently fuming over the prat on the phone in the quiet carriage, and moaning about the bank holiday rain...
And for you it will be different - it'll be things I've probably never noticed, but which are imperceptibly part of British life.
We're a multicultural nation, but immigrants expand and add to this tapestry, it's not as if they somehow delete it.