Does it matter? The absolute number of obese Brits will stay the same, so if you worry about the health of individuals, the average is kinda meaningless.
Unless you mean to say that without immigrants opening restaurant where healthy food is served, Brits will be back on traditional British foods, and become much more overweight as a result. 
There will be lots of agricultural work in Lincolnshire, Cambridgeshire and elsewhere. The locals clearly really want these jobs as they have been aggrieved by immigrants "stealing their jobs" for a long time. So, of course, they will be rushing to take these jobs and will consequently be much better off and healthier. Won't they?
Of course they will!
Reminds me of a cartoon I saw recently, where two German men, dressed as neonazis, shaven head and all, were happily cleaning a public toilet. Under the cartoon it said that the demonstration against foreigners stealing their jobs had been a full success for the two of them.
I am sure that's how it will be!