Conservative plans to rip up parliamentary convention in order to stack crucial Commons committees with Tory MPs will now have to overcome a Lib Dem blocking move.
Under current rules, the proportion of MPs on the standing committees that vote on legislation reflects the general election result.
Having failed to win a majority at the election, the Conservatives will not have a corresponding majority on the committees.
Downing Street insists changing this rule is “common sense”.
The prime minister’s spokesman said because the government has a “majority on the floor of the House” it was therefore “perfectly legitimate” it “should also have a majority in committees”.
But Jeremy Corbyn said it was an attempt to “rig” parliament as it would hand almost unprecedented power to a minority government.
And Lib Dem leader Vince Cable has tabled an amendment to the government motion due to be voted on by MPs on Tuesday, which would prevent the change.
Despite No.10′s claim, the government does not have an overall majority in the Commons.
Instead it is a minority government propped up in power by the eight Democratic Unionist Party (DUP) MPs who agreed to side with it on key votes.
With the help of the DUP, May has a working majority of just 13.
Asked if the party would support the government on its proposed change to the rules when it comes up for a vote on Tuesday, the DUP said it would not comment.
Ministers fear that all of their Commons business risks grinding to a halt or being gridlocked by Labour if the Conservatives do not control the committees.
The Lib Dem amendment to the government motion would block the change and keep the existing rules.
Cable said his party would work with other parties to “resist this attempt to undermine British democracy in the service of an extreme Brexit”.
“Eroding democratic institutions and rigging the rules in your favour is something we’d expect from a banana republic, not a Conservative government,” he said.
“Theresa May promised to act with humility and listen to the message sent by the British people after she lost her majority. It is now up to MPs to hold her to that promise and prevent this shameful power grab.”
The Lib Dems point out the prime minister said in June she would “respond with humility and resolve to the message the electorate sent” at the election.
Dr Ruth Fox, the director and head of research at the Hansard Society, told HuffPost UK Downing Street’s claim the government had a majority in the Commons was wrong,
However she noted the Conservatives were “by some distance the largest party” and there were “precedents” for what May was attempting to do.
“In 1974 a minority Labour government had a majority on the Committee of Selection,” she said.
“When John Major’s government lost its majority in the early 1990s Committee arrangements continued to reflect the majority position it had secured at the start of the Parliament.
“In 1976 the Labour government lost its majority when John Stonehouse MP crossed the floor but the Committee of Selection continued to operate as if it had a majority.
“When the Chair of that Committee subsequently died political disagreement about the balance between the parties did break out. But that was eventually settled by a motion not that dissimilar to Tuesday’s motion.”