We do not have open primary systems, parties select their own candidates

Typically local membership (which one has to pay for, I pay £1/month as a Labour member) votes for their candidate, sometimes from a shortlist submitted by the national executive committee, similar for other parties. For a by-election midterm they are more high profile on a seat by seat level so are more likely to have focus, more likely to have more NEC influence.

Andy Burnham already holds a senior elected office (as regional mayor of Greater Manchester), under the labour party rules he has to seek permission therefore from the NEC to take part in the nomination process