Hello there England,
Welcome to the forum :)
I'm just curious as to whether you regard yourselves as a "British Muslim." Are you proud to be British or is it just religion alone?
Islam teaches us that all people are equal regardless of where they are from or what their skin colour is:
O mankind! We have created you from a male and a female, and made you into nations and tribes, that you may know one another. Verily, the most honourable of you with Allâh is that (believer) who has At-Taqwa [i.e. one of the Muttaqûn (pious - see V.2:2). Verily, Allâh is All-Knowing, All-Aware. [Qur'an, 49:13]
The Prophet (peace be upon him) also said,
"O mankind, there is no superiority for an Arab over a non-Arab, or for a non-Arab over an Arab, or for a white over a black, or for a black over a white. All of you are descended from Adam and Adam has been created from dust of the ground" (Ahmad).
So in this sense, it does not matter (as far as I am aware) whether we are called British Muslims, Indian Muslims, British-Chinese, or whatever, if that is simply to denote where we are living or where we are originally from.
Do you support England in a sports games? Why is it that so many British Muslims rather support Pakistan when playing England at, say, cricket?
I think that varies from person to person, but people tend to have a close connection to their original countries and will often support them over the place that their family migrated to.
Do you find the Union Jack, St. George Cross offensive?
Due to its representing the Christian Cross, then of course I do not agree with it. But it is the right of a Christian country to bear the symbol of their choice on their flag, just as it is the right of others to sport their own. I wouldn't go waving it about myself though.
Peace :).