The German government is encouraging Britain to agree a mathematical formula for calculating its European divorce settlement rather than settling on a precise figure in an attempt to avoid a looming clash that risks derailing Brexit talks.

The chancellor, Angela Merkel, put the EU on a potential collision course with Theresa May on Thursday by insisting it made “no sense” to negotiate a future UK-EU relationship without first reaching agreement on the UK’s financial commitment to the EU.

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In her first big Brexit speech since May triggered article 50, Merkel told the German parliament that British politicians were still living under an “illusion” that the UK would retain most of its rights and privileges once it left the EU.

“Countries with a third country status – and that’s what Great Britain will be – cannot and will not have the same or even more rights as a member of the European Union,” she said. “You may think that all this is self-evident. But I have to put this so clearly because I get the impression that some in Great Britain still have illusions about this and that is a waste of time.”

There are mounting fears that the intransigent position of European leaders is encouraging the hardliners in Britain who are threatening to walk away with no deal. Britain’s CBI, German carmakers and the Irish government all sounded the alarm on Thursday at the dire prospects for UK-EU trade if there was no agreement.

Privately, officials in Berlin are looking for creative solutions to the problem, which might avoid the prime minister being forced to write a politically unpalatable €60bn (£51bn) cheque before she even gets to start negotiating future trade relations.

German government sources suggest that a “constructive solution” mentioned in Merkel’s blunt statement could take the form of the UK agreeing to a formula by which Britain’s future contributions in specific areas, such as pensions, EU budget, growth funds, would be calculated – thus avoiding coming up with concrete sums.

The idea was met with a mixture of bemusement and scepticism in London, where the Tory government remains determined to try to negotiate its future trade relationship at the same time as separation talks. Eurosceptic critics in the media are likely to calculate an implied cost of Brexit whether or not politicians are willing to acknowledge it publicly.

UK government sources pointed to earlier speeches by Merkel where she suggested there was merit in parallel talks. They suggested that the looming German election could be responsible for a hardening of language, which they hoped would be temporary. German taxpayers are likely to end up footing the largest bill for filling any EU budget shortfall after Brexit, leading to domestic pressure not to be seen to let Britain off the hook.

In the UK parliament, David Jones, the Brexit minister, told MPs that the government was willing to leave the EU with no deal if necessary.

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“The ambition and intention of the government is to achieve the best possible free trade agreement with our EU partners. However, our position also is this: we expect to negotiate toughly and, unlike the opposition, our position will be made clear to the European Union that we are prepared to walk away from the negotiating table if it is not possible to achieve a deal that suits us.”

Merkel was speaking shortly before European affairs ministers met in Luxembourg to finalise the negotiating guidelines EU leaders are due to adopt at a special summit on Saturday, the first ministerial talks without a British presence since 1973.

These guidelines flesh out the core principles of the EU’s negotiating strategy: preserving the single market and stopping the UK from “cherrypicking” the EU’s advantages, as well as a ban on talks about a future trade deal until the UK agrees its EU divorce, including paying the Brexit bill.

With the text largely agreed, the meeting served as a show of unity before Brexit talks. “It was an unprecedented signal of trust, unity and consensus” of the 27 EU member states, declared Louis Grech, the deputy prime minister of Malta, who chaired the meeting. “All delegations agreed with the overall thrust of the guidelines and expressed their full support. We made it very clear in the guidelines that the single market is indivisible and [there] will not be cherrypicking.”

Responding to a question about the UK contributions to the EU budget, he said the financial settlement had not been discussed in detail.