I would say far more than what we imagine - it doesn't affect our deen, it in fact determines our deen.
The term deen refers to a way of life, a lifeway, a civilisation and not a religion. Religion is a modern term that most historic civilisations would never recognise. A set of dogma and rituals that are allowed to be practiced in the personal sphere by a secular political elite who distance the divine from any collective matter in the social, civic or political realm.
Islam as a deen was completed in Medina where a new way of life and civilisation emerged. Its members were labelled Muslims. They lived a divinely ordained way of life in all aspects of their lives - shaped by a collective culture, institutions, laws and norms determined by revelation.
We think we follow Islam living in Birtain and are British Muslims but the reality is we follow Nationalistic Liberal Secular ideologies with an Islam that has been amputated to fit, reduced to a personal religion complete with dogma that make little sense to most in a secular society.
The sad reality is our Deen is "Liberal Secular Islam" and we are "BritishMuslims".
A far cry from Islam being our deen and us being Muslims.
And before those abroad start patting themselves on their backs, you too are colonised and leading similar depressing ways of life... PakistaniMuslims, SaudiMuslims, EgyptianMuslims, YemeniMuslims etc.
Can we live anywhere as Muslims?
We can't - every country has become a total mess. We are where we are, we do our best whereever we are and we need to strive to bring about change like the Prophet (saw) and his companions did in Mecca when revelation commenced and the Quraysh dominated society with their way of life.