It is true that Britain has had much immigration from Europe and elsewhere since the medieval period for many reasons of which religious persecution is one This is set out in the article Historical immigration to Great Britain However you have provided no evidence for your assertion that Britain is foremost an immigrant country by which I assume you mean that most of the current population derives from post medieval immigration I very much doubt whether that is the case I think that most of the population is descended from pre medieval or medieval immigrants as set out under Genetic history of the British Isles But it would be useful for a reliable source to be provided which quantifies the proportions of Britain s genetic heritage from different sources Does such a reference exist