Andy Burnham will push to become prime minister in time to address Labour’s autumn party conference in Liverpool, his supporters have said. The Greater Manchester mayor cleared his first hurdle to becoming the candidate in the Makerfield byelection on Friday as Labour’s ruling body gave him permission to stand for the seat. If confirmed as Labour’s choice, he will need to win a difficult byelection in the Greater Manchester seat in mid to late June, with support for Reform UK having surged in the area at the local elections. With the byelection most likely to take place on 18 June, some of Burnham’s supporters believe he has a path to becoming prime minister before parliament breaks for the summer recess, but sources close the mayor’s campaign believe his preference is a longer timeline. The prize for Burnham winning a leadership contest in the summer would be a victorious homecoming and what one supporter described as a “natural moment” for a transfer of power in the north-west city.…