Leeds West MP Rachel Reeves joined Wigan’s Lisa Nandy to write to BBC Director General Lord Hall over the “inexplicable” move.
The programme said Thursday’s show was broadcast from Dulwich to allow politicians attending Brexit debates at Westminster to take part.
Some social media users said moving filming from Bolton, where 58 per cent voted to leave the EU, ensured a pro-EU audience in London, which voted to remain.
But the BBC rejected suggestions moving the show was related to the way Bolton voted in the referendum.
A spokesman said: ““The decision was taken at the start of the week when it was extremely unclear when and if crucial Brexit votes would be taking place.
“If there had been voting on Thursday, politicians would not have been able to get to Bolton.
“For a range of logistical reasons the decision had to be made early in the week.
“We are working with the venue in Bolton to find another suitable date and look forward to broadcasting there in due course.”
In their letter, Ms Reeves and Ms Nandy wrote: “We find it inexplicable that the event did not take place in Bolton as intended.
“There were no votes in the House of Commons and even if there had been, business in Parliament finishes at 5pm on Thursday.
“Given that the panelists were largely from London, we think the nation might have benefitted from some non-London centric views on the programme.”
The Labour MPs added in their letter: “Question Time is an important part of our national political debate and one of the few national programmes that allows any voice for people outside of London.
“With very little respect for, or understanding of, what is happening to our country outside of London in the national debate, this decision has caused real anger in our constituencies, and in many parts of the country.”