Rachel Reeves, the MP for Leeds West, and Lisa Nandy, MP for Wigan, have written to the corporation’s boss to express their fury at the decision.
The producers of the popular talk show changed the venue from Bolton’s Albert Halls to the James Allen’s Girls’ School, in Dulwich, south London, which can cost parents up to £17,991 a year.
It was said the change of plan, which was made at the beginning of the week, allowed politicians who were invited to appear on the programme to also attend any Brexit debates that might happen in Westminster.
But the Labour MPs blasted the excuse. “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 finished at 5pm on Thursday,” they wrote in a joint letter.
Highlighting the change of venues, the MPs questioned why producers awarded the “prestigious” event to a fee-charging institution.
“Schools like this benefit from a large number of prestigious events and if the event needed to take place in Dulwich could you not have looked to secure one of two local state schools”, they wrote.
The change in venue was spotted by angry viewers who accused the corporation of bias.
The weekly debate, hosted by presenter Fiona Bruce, is filmed as though it is live a few hours ahead of its broadcast after the 10pm news bulletin on BBC One.
Thursday’s edition saw the culture secretary, Jeremy Wright, David Lammy, MP for Tottenham, and left-wing journalist Ash Sarkar on the panel.
A BBC spokesperson said in a statement: “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.”
This article was updated with further information from the BBC and a statement from a spokesperson.