The previous PM, David Cameron resigned in direct response to the No vote in the EU Referendum. He had consistently campaigned to stay in the EU. On his resignation David Cameron stated that it would be wrong for him to be the captain that steers our country to its next destination". But how Brexit exactly is the new PM, Theresa May? She campaigned alongside David Cameron in favour of staying in the EU. EU referendum: David Cameron wins Theresa May's backing So why bother changing PM's since they both campaigned to stay in Europe. Does this really make sense?