Craig Kieswetter is no doubt going to get thoroughly sick of being asked whether he feels English, even though it's the wrong question. Like me, he has one British parent and one foreign, which makes him as British by descent as I, though since his mother is a Scot and my father was English, I'm English and he isn't. He can hardly sit there at a press conference unveiling him as an England player and say he doesn't feel "English", but he ought to feel offended to have to confess to Sassenach loyalties. Robert Croft, the former England Test player, used to make a big point of not being English but Welsh – but then he had been born and raised in Wales, so nobody expected him to pretend to be English.
When someone has a choice of which nationality to adopt, in cricketing terms it makes sense to opt for British nationality: unless you can get on to the international circuit or get offered an IPL contract, county cricket is the most lucrative source of employment available. They decide to go through a qualification period not because they believe they will be selected for England more easily than for the country where they did most of their growing-up, but because it is the passport to fifteen years of being able to make a comfortable living playing cricket rather than stacking supermarket shelves.
Once they are qualified, though, it makes little sense for the England selectors to ignore them just because they were born abroad. And if it seems that too many immigrants are turning up in the England side, it's hardly the immigrants' fault that they're so good: the question, if any, is why people growing up in England don't seem to develop into top-level players, especially batsmen. It's a pretty complex question, but that most people in Britain now live in densely-populated cities with very limited space given over to playing fields, parks and so on, particularly in comparison to people-poor, land-rich Australia or South Africa, must be a major contributing factor – and there is little the ECB can do about that.