Brexit talks have become deadlocked with the UK and EU negotiating teams failing to make progress in a string of critical areas, The Independent understands.

As the third round of discussions closes on Thursday, the British team are increasingly certain that the hands of EU chief negotiator Michel Barnier are tied by the rigidly worded mandate handed to him by the EU27 member states.

Intense discussions on Tuesday and Wednesday underlined how the biggest stumbling block is the UK’s “divorce bill”, with Britain and the EU diametrically opposed over how to calculate the settlement.

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Other issues, including whether Britons will keep their European Health Insurance Cards and what happens to the movement of British goods immediately after Brexit, are also said to be causing difficulty.

The limited progress of the latest round of talks come amid reports that Theresa May is planning to appeal directly to national leaders in a bid to break the impasse.

British officials believe that the mandate given to Mr Barnier has prevented him having sufficient space to negotiate progress, in particular robbing him of the ability to move on to future trade relations, before separation issues like the divorce bill, citizens’ rights, and the Northern Ireland border are addressed.

The UK team believes the distinction between future relations and withdrawal is artificial, and that a greater degree of parallel negotiations must be allowed.

The settlement of Britain’s financial obligations is also a particular sticking point, with the UK wanting to go through specific areas where the country could owe money and calculate any figure from the “bottom up”, while the EU wants a more top-down approach based on an overarching calculation of what the nation should pay.

The attempt to shift the blame for a lack of progress on to the EU comes after Commission chief negotiator Mr Barnier said he was “worried” about UK “ambiguity” on certain issues and Commission president Jean-Claude Juncker said Britain’s preparation for the talks was not “satisfactory”, while European Parliament president Antonio Tajani is the latest to add his name to the list of EU chiefs berating the UK, accusing it of causing “uncertainty”.

Senior EU officials say Mr Barnier’s negotiating team is simply taking the approach the European Council and the 27 remaining member states have instructed them to take – but both sides increasingly agree, behind closed doors, that this month’s round of talks are about clarifying and understanding one-another’s positions – with limited concrete progress beyond that expected to be made.

Mr Barnier said today that the guidelines given to him by the EU27 were “designed for serious and constructive negotiations, but we need clear UK positions on all issues”.

Asked how the negotiations were going, a European Commission spokesperson told reporters in Brussels on Wednesday: “They are continuing.”

The lack of significant progress further hardens the possibility that the two sides will not make what the EU calls “sufficient progress” by October to move onto trade talks about the future UK-EU relationship – though UK officials still think they can meet the EU’s threshold to begin the next phase.

The two sides will together make an official statement on Thursday setting out what they have achieved. The next round of talks are due to start on 18 September, with a fifth round in early October – after which the EU will decide if trade issues and Britain’s future relationship with the EU can start to be addressed.

Brussels officials today also poured cold water on a reported plan from Downing Street to bypass Mr Barnier’s negotiating team and instead go straight to member states like France and Germany. An official pointed to the instructions drawn up by the member states, which say negotiations are to be conducted as “as a single package” where “individual items cannot be settled separately”.

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A source familiar with the UK’s negotiating position said: “There is some concern about what the UK says is an inflexibility to the Commission’s approach, that it’s difficult to negotiate with people who have perhaps not been given the flexibility to negotiate.”

The French government earlier this week stood by Mr Barnier’s team, saying that it “fully supports, on the substance as well as on the method, Michel Barnier’s negotiating mandate” and that suggestions in the British eurosceptic press that it would bypass him “are founded on absolutely nothing and do not reflect reality”.

It comes as Theresa May insisted the UK was making the running in the talks.

“We have been publishing a series of papers over the summer, there will be more papers to come, where we are setting out the key issues that both sides need to address, the options that we have, the ideas we have, of how to deal with those,” she told the BBC.

“It’s the United Kingdom that has been coming forward with the ideas and with the clarity about the future.”