Dame Margaret Beckett said leaving the EU was "the most difficult decision we've made possibly for hundreds of years" and John Bercow should be allowed to continue in his post as "this is not a normal time for a speaker to stand aside".
MPs have called for Mr Bercow to to resign in the wake of a damning report by former high court judge Dame Laura Cox, which laid bare the “urgent and serious problem” of sexual harassment, intimidation and bullying in Parliament.
More than 200 complainants claimed to have been groped and propositioned, often by male MPs, amid a culture of “deference, subservience, acquiescence and silence”.
The report said it was “difficult to envisage” that reforms could be delivered under the current administration, of which Mr Bercow is one of the most senior figures. He has also faced separate allegations of bullying by former aides, which he strongly denies.
Dame Margaret said changing speaker at this time would "add to the list of disasters we have inflicted upon ourselves of late".
Asked if she was condoning the behaviour, the former foreign secretary told the BBC's PM programme: “Alright, yes. I will answer your question bluntly and directly.
"Abuse is terrible, it shouldn't happen, it should be stopped, behaviour should change anyway - whether the speaker goes or not.
"But yes, if it comes to it, the constitutional future of this country - the most difficult decision we’ve made not just since the war but... possibly for hundreds of years - yes, it trumps bad behaviour.”
The Derby South MP said she could not think of a "more disastrous time" for a new and inexperienced speaker to take up the position, ahead of potential parliamentary clashes over Brexit.
She added: "There are always possibilities that the speaker can, as presiding chair, be forced into a position of taking a major decision on behalf of the country as a whole.
"And if there is ever likely to be such a time, it is likely to be in the coming months."
Earlier, shadow foreign secretary Emily Thornberry came under fire for throwing her support behind Mr Bercow.
She told Sky News: "I think this is absolutely not the time to be changing Speaker. We don't know, for example, with regard to Brexit, as to what is going to happen."
Dave Penman, general secretary of the FDA, which represents senior civil servants, described Ms Thornberry as "completely disingenuous".
He said: "Just last month, you were speaking at the TUC 150th Anniversary dinner about workers' rights.
"Now you're happy to ignore Dame Laura Cox's urgent calls and put party politics before people. Which side are you on?"
Mr Bercow has signalled that he will stand down next summer, after a decade in the post, to see the Brexit process through the Commons.
However he failed to respond to calls to quit immediately, despite a direct challenge from Tory equalities committee chair Maria Miller.
Speaking during a Commons debate, she said: "The report is clear that there needs to be a complete change in leadership at the most senior level, including you, Mr Speaker, as chief officer, if we are, in Dame Laura’s words, to press the reset button.”
Tory MP Anne Main also said: “It’s the old adage that the fish rots from the head, and the leadership failings that have been highlighted in this report are extremely worrying.
“The important thing is nobody need fear to be able to call into account those, however senior they are, if they have failings.
“If this report has identified senior leadership failings ... no one should be involved in this process who has been potentially linked to being part of the problem in this process.”
Ahead of a parliamentary clash, Mr Bercow said he wanted all complaints about abuse to be investigated by an external independent body.
Mr Bercow said: “I firmly believe that the only possible way to resolve this matter is the establishment of a body which is both entirely independent of and external to Parliament, to hear and adjudicate upon all allegations of bullying, harassment and sexual misconduct, including deciding how far to investigate past misconduct.”
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