Depends on the definition of British and non-British. I think council houses should be allocated according to the needs of both British people and immigrants who have acquired the right to stay here forever. An African family with two children who are homeless should obviously be given the right over a newly married British couple who are currently with their parents.
Having said that, both of those examples should, in my view, have priority over immigrants who don't have the right to stay here indefinitely. I.e. temporary immigrants that will leave after so-many years or those who are awaiting deportation.