The Independent understands Ms May won the backing of key cabinet figures to almost double the amount being offered by the UK to settle its financial obligations in Brussels.
But the Prime Minister agreed with her ministers that the extra money must be conditional on securing an acceptable transition deal and a good free trade agreement.
The move marks a key development in the UK’s approach and opens the way for EU leaders to approve in December the start of talks on a trade deal that would be critical to Britain’s post-Brexit prosperity.
With the clock ticking until the UK drops out of the EU in March 2019, Ms May has been under intense pressure to ensure Brussels agrees to allow trade talks to begin at the summit of the European Council on 14 and 15 December.
But while the EU has been demanding more money as its price, Ms May knows Brexit-backing members of her Cabinet, like Michael Gove and Boris Johnson, and some hard-line Tory backbenchers will not forgive handing Brussels a huge pay-off.
A proposal agreed at Monday’s Brexit cabinet sub-committee meeting, to be fleshed out this week, will see a “something for something” approach, with a bigger divorce bill accepted in return for concrete movement on trade and transition.
Ms May will not make an open offer yet or set out a clear figure when she does. Instead it is likely to see her give more detail to EU leaders on how the UK believes the final bill for the UK’s liabilities should be calculated – amounting to a further £20bn.
This comes on top of indications given in her speech in Florence in September that would see the UK pay an initial £20bn.
There were also reports that the UK Government could still allow the European Court of Justice a role in protecting the rights of three million EU citizens.
A Downing Street source underlined the importance of the EU agreeing to allow trade and transition talks at the same time as the offer from the UK being made.
He said: “It remains our position that nothing's agreed until everything's agreed in negotiations with the EU.
“As the Prime Minister said this morning, the UK and the EU should step forward together.”
Ms May is set to meet European Council President Donald Tusk on Friday and will be able to discuss the development on the divorce bill as well as the future of the Irish border and EU citizens right – the three key issues on which progress is needed.
Ms May had emphasised the need to synchronise moves forward with Brussels during a trip to Birmingham with two cabinet ministers taking a more cautious approach to Brexit, Chancellor Philip Hammond and Business Secretary Greg Clark.
She said: “What I want to see is developing that deep and special partnership with the EU for the future and I want to see us moving together because as I’ve always said, a deal that’s good for the UK will be good for the European Union.”
Mr Hammond underlined the urgent need to secure a post-Brexit implementation period in the next few months, acknowledging it was a “wasting asset” that would have less value the later it was agreed.
The Chancellor said it would be “much less useful” in a year's time as businesses would have started making alternative arrangements and government agencies would have begun putting in place contingency plans ahead of the expected Brexit date on 29 March 2019.
But Conservative ex-minister Robert Halfon said the public would go “bananas” if the UK offered £40 to £50bn at a time of constraints on public spending.
Tory Brexiteer Jacob Rees-Mogg urged the Government not to fall into a “trap” on the divorce bill, and argued the UK should use the EU’s need to fill holes in its budget as leverage.
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