Even if they go on a deportation spree to rid themselves of offending migrants, the population of naturalized Muslims is already enough to ensure Brits would be a minority. Their birth rate is low anyway, just like most of Europe.
It is not just the high number of births. The Muslim population in England is increasing due to a wide range of reasons. A lot of people are converting to Islam, mostly in prisons and drug rehab centers. Also, a lot of non-Muslim women are marrying Muslim men and then converting to Islam.