Theresa May will come under pressure from Brexit supporters in the cabinet to spell out what she hopes the UK will gain from paying the EU a higher divorce bill of about £40bn, as her most senior ministers meet to discuss an improved offer.

The prime minister will attempt to reach a consensus over a proposed offer at a meeting of her cabinet committee on EU strategy on Monday as the UK tries to break the deadlock in Brexit negotiations.

But some of the leave-supporting ministers, including Boris Johnson and Michael Gove, are understood to be applying pressure behind the scenes to make sure that the UK has a clear idea what it wants from a future trading relationship before agreeing to hand over such a large sum.

They are likely to press the prime minister to begin cabinet discussions on the UK’s future trading relationship after the pair sent a joint letter to No 10 in recent weeks demanding an arrangement that allows Britain a wide degree of regulatory freedom.

Philip Hammond confirmed on Sunday that the UK would make an improved offer to the EU within three and a half weeks, after Michel Barnier, the EU’s chief negotiator in Brussels, said Britain had a fortnight to break the impasse.

“We will make our proposals to the European Union in time for the council [on 14 December], I am sure about that,” the chancellor told the BBC’s Andrew Marr Show. He promised Britain would honour its debts but also “negotiate hard” on the various aspects of the financial settlement.

However, senior Brexiters are particularly concerned about the idea of signing over a high sum as part of the withdrawal agreement but later ending up with an unsatisfactory deal on the future relationship.

Johnson is not thought to be opposed in principle to a divorce bill higher than the £20bn already offered by May but would need assurances that the UK was heading for the right type of relationship with the EU when it leaves. At the moment, there is a cabinet agreement on seeking a two-year transitional period after Britain leaves the EU in March 2019, but nothing has been agreed on what the future relationship should look like after that.

Q&A What is a hard Brexit? Show A hard Brexit would take Britain out of the EU’s single market and customs union and ends its obligations to respect the four freedoms, make big EU budget payments and accept the jurisdiction of the ECJ: what Brexiters mean by “taking back control” of Britain’s borders, laws and money. It would mean a return of trade tariffs, depending on what (if any) FTA was agreed. See our full Brexit phrasebook.

Some in the former remain wing of the Conservative party are also keen to see clarity in terms of what the UK will achieve by agreeing to pay a higher amount. Stephen Hammond, one of the Conservative MPs opposing a hard Brexit, told the BBC’s Sunday Politics: “I think where we have to be clear is what we’re paying for and what we’re getting. No one is suggesting that we should just hand over money without any proper scrutiny. That would be entirely inappropriate. But it may well be entirely appropriate to put in money to facilitate international trade which will secure jobs in this country.”

May’s meeting comes at a time of continuing tensions over Brexit within the cabinet, including reports that David Davis, the Brexit secretary, was pushed to the brink of resignation by being excluded from Johnson and Gove’s letter to the prime minister making demands over her strategy.

A source close to Davis strongly denied that he had any intention of walking out, saying: “This is completely wrong and anyone pushing this nonsense in order to undermine Brexit is going to be sorely disappointed.”

However, the demanding tone of Johnson and Gove’s letter raised eyebrows among their senior colleagues. May has agreed to one of its requests – a Brexit taskforce on implementation – but Johnson has been left off the list of those on the new subcommittee on preparations for leaving the EU.

Dominic Grieve: the former attorney general said some Tory colleagues had ‘become unhinged’ over Brexit. Photograph: Christopher Thomond/The Guardian

May is also facing the continuing parliamentary battles over the EU withdrawal bill on Tuesday. The most significant vote of the week will be over the issue of human rights, led by the former attorney general Dominic Grieve as he attempts to get the EU charter of fundamental rights incorporated into UK law. The senior Tory may withdraw his amendment if the government makes concessions to safeguard human rights.

But Grieve, who is battling to stop May fixing the Brexit date of 29 March 2019 in law, told BBC Radio 5 Live that some of his colleagues, though not the prime minister, had “become unhinged” over the issue of leaving the EU.

“The prime minister’s problem is that she’s surrounded by people who get louder and more strident by the moment as some of the inevitable problems which were going to come with Brexit start to make themselves apparent,” he said.

On the other side, Suella Fernandes and John Penrose, two Tory MPs involved in the strongly pro-Brexit European Research Group, accused rebels of trying to “torpedo” Britain’s withdrawal from the EU.

They said the legislation should be a “spectacularly simple” legal “copying and pasting” of EU law in UK law but claimed there was a “danger it will be used as a Trojan horse, to thwart the referendum result by stealth”.

“The issue isn’t really the date: it’s the timing of a vote on the final deal that’s being negotiated with Brussels,” they wrote in a joint article for the Sunday Telegraph.

“If the deal isn’t agreed until the two-year article 50 timetable is up (and whoever heard of an EU negotiation or summit finishing early, after all?) then the vote can only be ‘please choose between this deal or no deal at all’.”