The government wants the option of extending the Brexit transition period up to the end of 2022, the business secretary, Greg Clark, has said, a move likely to further enrage the Conservative party plotters who hope to remove Theresa May this week.

Amid predictions from hardline Brexit-backing Tories that the crucial mark of 48 MPs seeking to depose May could be reached on Monday, Clark endorsed an idea raised by the EU’s chief Brexit negotiator, Michel Barnier, which could keep the UK tied to Brussels rules for up to two further years.

At a meeting of ambassadors from the EU’s 27 member states, Barnier proposed the idea of extending the transition period beyond the agreed 21-month limit, taking it to December 2022, allowing two extra years to negotiate the relationship.

Asked about the idea, Clark said the option of extending the transition period at “our discretion” could help businesses having to potentially change working practices twice, but avoiding the chance of the backstop guarantee coming into force if a final trade deal had not been sealed in December 2020.

“Businesses, especially small businesses, have said very clearly that they would much prefer to have one change, rather than have to change things twice, to two different regimes,” he told BBC Radio 4’s Today programme.

“It would be at our request, and that would be a maximum period. But it would be for this purpose – if the negotiations are making good progress but haven’t quite been finalised, to have the option – and it would be an option for us, and there is value in having an option – in rather than going in for a temporary period into the backstop and having a second change, to have the option, if the UK wanted, to extend the transition period.”

Asked if this meant the transition period could extend, as detailed by Barnier, to the end of 2022, Clark did not reject this, saying: “The point is that if we have the option we don’t have to use it. Our strong preference is clearly to complete the negotiations.”

The idea is seemingly intended to appeal to businesses, before May addresses the CBI business group conference on Monday morning, as she seeks to resume control of the political narrative after a bruising week.

May travels to Brussels later this week to hammer out the final details of the political declaration on Britain’s future relationship, in the hope the whole package can be approved at a special EU summit next Sunday.

But the idea of the UK following EU rules and paying into its budget with no say on how the bloc operates for up to six-and-a-half years after the 2016 referendum is likely to infuriate discontented MPs, as well as alarm some of May’s other ministers.

MPs from the Brexit-backing European Research Group reiterated on Monday that this still hoped to force a no-confidence motion on May by gathering the 48 MPs’ letters they needed, to be sent to Graham Brady, chair of the backbench 1922 Committee.

One ERG member, Newton Abbot MP Anne Marie Morris, told BBC1’s Breakfast there was “no question” the threshold of 48 letters would be reached this week. She said May “has had one of the most difficult jobs” to do, and that the prime minister is “not going to deliver Brexit”.

Simon Clarke, the Middlesbrough South and East Cleveland MP and another ERG member, urged fellow MPs to act immediately.

“Today is I think a really important day in that process, because colleagues who had said that they will act now need to search their consciences and follow up on what they’ve pledged to do,” he told Today. “This day must be the day at which action is taken. We now have a deal on the table, it’s gone from theory to reality, and our worst fears have been realised.

“Every hour, every day, that we delay the moment of reckoning on this, every day that elapses without having rejected this deal is one day less to embark either on credible negotiations to try and remove the backstop that is the issue at the heart of these negotiations, or failing that prepare with an intensity that we simply have not seen for a no-deal scenario.”

As well as the threat of being ousted, May faces pressure from a group of cabinet ministers who have stayed in her government but hope to persuade her to seek an amended deal with Brussels, including the Commons leader, Andrea Leadsom, the international development secretary, Penny Mordaunt, and the environment secretary, Michael Gove.

But in his interview, Clark dismissed the idea that the deal could be changed at this stage. He said: “If you think about the time that’s gone into that negotiation, and the detail it comprises, I think this deal – which is a good one in my view – is the one that will go to the European council.”

Asked if the outline for a future relationship could be changed, he added: “Not in any substantive sense.”