William Hague has tabled a change to parliamentary procedures to make it easier for Tory opponents of the Commons Speaker, John Bercow, to unseat him after the election.

In a move described by the shadow leader of the Commons, Angela Eagle, as a “grubby” plot, Hague will use his last day as an MP after 26 years at Westminster to allow MPs to vote on whether a secret ballot should be held on Bercow’s future after the election.

The Tories, who agreed with the Liberal Democrats to hold the vote in government time on Thursday – the final day of parliament before the election – came under fire for underhand tactics after slipping out the motion on Wednesday evening. Many Labour MPs had by then returned to their constituencies to campaign in the runup to the election.

Tory sources said that Hague is simply giving MPs the chance to vote on a recommendation by the Commons procedure committee. Members of the committee said that MPs should be allowed to decide on whether the election of the Speaker, which takes place at the start of every parliament, should be held by secret ballot.

Bercow’s opponents have long campaigned for the right to turn the traditional post-election vote into a secret ballot. The Speaker’s critics believe that only a handful of MPs would be prepared to register their opposition to Bercow under the current system in which the Father of the House takes the chair in the first parliamentary sitting after the general election. An incumbent Speaker would normally expect to be re-elected on the nod. A secret ballot would allow MPs to vote against the Speaker without fear of repercussions if he wins.

Tory and Lib Dem sources rejected Labour claims they had acted in an underhand way. They said they were following the convention of allowing MPs to vote on the recommendations of the procedure committee. But Nick Clegg, who is spending the day in his Sheffield Hallam constituency after his weekly LBC phone-in, will not be present for the vote.

Michael Gove, the Tory chief whip who is often rebuked by the Speaker, has made careful preparations to ensure there is a strong turn out of Tory MPs for the vote. In common with all votes on parliamentary business, MPs will be given a free vote which allows them to vote as they like. But Gove has imposed a three-line whip to compel Tory MPs to attend a briefing at 10.30am by Lynton Crosby, the Tory campaign director. This means that large numbers of Tory MPs will be at Westminster for the vote which is due to be held around 11.30am.

Tories said that the decision to hold the vote was seen as a gesture by Downing Street to Tory backbenchers, particularly those on the right, who do not like Bercow. They say that the Speaker, who was elected as the Tory MP for Buckingham in 1997, won election in 2009 on the basis of strong support from Labour.

The prime minister, who received a warm reception on Wednesday from Tory MPs at the 1922 committee’s last meeting before the election, is keen to reach out to his Tory critics. Downing Street is nervous that disaffected Tory MPs could try and unseat him at a meeting of the committee after the election, to be held on 11 May, if he fails to secure a decisive win over Labour.

Downing Street would not be sorry to see the Speaker go. Bercow regularly admonishes the prime minister and thinks nothing of hauling ministers before MPs to answer urgent questions.

Eagle condemned the Tory tactics. “This is a grubby last-minute plot in the dying hours of this parliament to try and change the procedures of the House. The Tories are trying to play politics with the Speakership because they know they won’t win a majority at the next election, and the Lib Dems appear to have signed up to it.”

Ben Bradshaw, the former Labour culture secretary, tweeted: “Sneaky/cowardly of Tories/Libs to turn to secrecy in bid to oust Speaker who’s championed back benchers & made Commons much more relevant.”

Chris Bryant, the shadow arts minister who has written a book on the history of parliament, tweeted: “Particularly shabby of @WilliamJHague as he’s not standing and has no mandate for this motion. Gratuitous cowardly attack on Speaker.”