Theresa May should think back to Margaret Thatcher’s fight for a UK rebate from Brussels as she battles a multibillion pound Brexit divorce bill from the EU, Boris Johnson has suggested.

The foreign secretary – referring to the actions of the former Conservative prime minister – appeared to apply pressure on May to stand firm against EU demands for cash, amid reports saying the UK could be asked to hand over up to £50bn as an exit fee.

Asked about that prospect, Johnson said: “I think we have illustrious precedent in this matter: I think you can recall the 1984 Fontainebleau summit in which Mrs Thatcher said she wanted her money back and I think that is exactly what we will get.”

He told a BBC2 programme, Brexit: Britain’s Biggest Deal, that the UK should not have to make large payments to the EU after leaving the union.

“It is not reasonable, I don’t think, for the UK having left the EU to continue to make vast budget payments. I think everybody understands that and that’s the reality,” he said.

Downing Street has not ruled out the idea of paying either a “divorce settlement” or continuing some contributions, saying the UK is only at the beginning of the Brexit process and negotiations have not yet started.

As May attended an EU council summit in Brussels on Thursday, she was asked directly if she would refuse to pay a divorce bill.

“Let me be very clear, there is only one Margaret Thatcher, but if it comes to the issue of comments about paying money into the EU, Boris is clear and I am clear, when people voted to leave the European Union, they voted for us in the future not paying huge sums of money into the EU every year. Of course when we leave the EU, that will be the case,” she said.

Formal talks cannot begin until May’s Brexit legislation clears parliament and the UK triggers article 50, which could come as soon as Tuesday in the form of a letter to the EU council president, Donald Tusk.

However, EU leaders have started to address the issue of the UK having to pay to wind up its liabilities. Arriving at the EU summit, Enda Kenny, the Irish taoiseach, indicated that he would back demands for Britain to pay a divorce fee.

“When you sign on for a contract, you commit yourself to participation. And obviously the extent of that level of money will be determined,” he said.

The European commission’s chief Brexit negotiator, Michel Barnier, has reportedly discussed the figure with European leaders ahead of the crucial talks.

He tweeted a picture from a meeting with Rumen Radev, the president of Bulgaria – the country that will hold the EU presidency for the first six months of 2018 – saying they had a “common position” on citizens, the budget and unity of the 27 nations in the EU.

May is also facing a potential battle over a recommendation that the UK pays a £1.7bn fine for negligently failing to stop European markets being flooded with fraudulent goods from overseas criminal gangs.

The European fraud watchdog, Olaf, has recommended the fine be imposed by the European commission, but the UK is disputing the finding.

May’s ambition to strike a trade deal with the EU within two years in parallel to Brexit divorce negotiations was also questioned at the summit by the Danish foreign minister, who said it could take up to 15 years.

Anders Samuelsen told Bloomberg: “You have to find a solution and we will find a solution. The question is, can we do it in two years or will we take 15 years? We don’t know.”

Pressed on whether two years was realistic for a trade deal, May said: “The process which article 50 sets out is for the withdrawal but also setting the framework for a future relationship, which actually should take the two years.

“That is the timetable we’re working to and the EU is working to. I am optimistic we can achieve a good and comprehensive trade deal with the EU.”