Senior backbenchers accused him of making the decision so that Sir Keir Starmer could avoid the prospect of an embarrassing Labour rebellion.
Sir Lindsay rejected those accusations and insisted that he had been motivated by the fact that MPs were facing threats to their safety over the vote.
He subsequently apologised for the “mistake” and last Thursday offered to use his powers to grant an emergency debate on the same topic.
But he backtracked when pressed on the pledge by Mr Flynn on Monday, telling him: “I have decided the application for an emergency debate should not proceed.”
Sir Lindsay explained that his decision had been made because the Government was set to make a “relevant statement” in the Commons on Tuesday.
He added that his clerks agreed with the decision, unlike last Wednesday when he overrode their advice to break Commons convention and allow Labour’s amendment.
Update on situation in Gaza
Andrew Mitchell, the Development Minister, was set to deliver an update on the situation in Gaza, though there were no plans for any vote to be held on a ceasefire.
Mr Flynn, who has already said that he thinks the Speaker should quit, said the decision “called into question” the trust placed in him by MPs.
”Last week the Speaker of the House of Commons broke the rules, this week he has broken his word,” he said in a statement.
”The fact that that has been blocked is outrageous, it flies in the face of what we were told would happen last Thursday. I think the public will be as outraged as I am.
‘‘I would imagine that parliamentarians across the chamber will be deeply concerned about the fact that the Speaker has made a clear and unambiguous statement that he would have a debate and a vote in relation to the situation in Gaza and that he has instead opted not to do that.”
New signatories on Monday
The fresh row will add to pressure on Sir Lindsay, who has faced sustained calls to step down since he was forced to apologise for last Wednesday’s chaos.
A motion tabled by William Wragg, a Tory MP, expressing no confidence in him as Speaker had attracted the signatures of 80 MPs on Monday night.
The new signatories on Monday included Rachel Maclean, a deputy chairman of the Conservatives, and former foreign office minister Vicky Ford. It meant that almost one in eight MPs have now called for Sir Lindsay to go.