Ministers who control the House of Commons schedule have blocked Labour's plans to hold a "no-confidence" vote in Boris Johnson, the government and Labour.
Downing Street stated that it would allow for time for a vote in no confidence in government but not the prime minster.
A spokesperson for the PM said that he had already declared his intention to quit, and that a vote wouldn't be a "valuable usage" of MPs time.
Labour accused ministers, however, of being "run scared".
Ministers must allow MPs time to vote on motions from the official opposition that express their dissatisfaction with the government, as per Parliamentary conventions.
Erskine May, the bible of parliamentary procedures, gives examples of confidence motions in the past but doesn't give precise rules about what counts as a no confidence votes.
However, Nigel Evans, Deputy Speaker, stated that the government had determined that Labour's motion couldn't be taken as such.
Nikki da Costa was a former advisor to No 10. She said Labour's motion wasn't a traditional confidence vote and therefore didn't pass the test.
Labour argues that motions to no confidence "can take many forms". They point out one example from 1965, which stated: "This House does not have confidence in Her Majesty’s Government and condemns the conduct of the prime minister in the affairs of the nation."
Sir Keir Starmer, Labour leader, stated earlier Tuesday that he wants a vote to stop Mr Johnson "clinging to for a few months after his own MPs forced his resignation".
"We have submitted a vote to no confidence and challenged any Tory MP that in the past few days said, 'I cannot serve Boris Johnson because I can't trust one word the man says'.
"Can they vote to tell him to stay in power for a few more weeks?"
The Labour motion had been submitted on Tuesday and was expected to be voted on Wednesday.
The motion stated that "This House does not have confidence in Her Majesty’s government while the Rt Hon Member from Uxbridge or South Ruislip is Prime Minister."
The government refused to allow time for voting, saying that "They [Labour] have decided to play politics by submitting a vote de no confidence in the government's leadership and the prime minister.
"As the prime Minister has already resigned, and a leadership transition is underway, we don't feel that this is a worthwhile use of parliamentary space. "Should Labour make any amendments to their motion, they will have the next business day to discuss it."
Labour retorted, accusing Conservatives of "changing rules to protect their dodgy mates".
On Thursday, Mr Johnson resigned as Tory leader but said that he would remain as prime minister until a successor is found.
On 5 September, the next Conservative leader and prime minister will be announced.
