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Theresa May has warned she will not sign up to a Brexit "agreement at any cost" as she said "significant" issues continue to block the path to a deal with Brussels.

The Prime Minister used a speech to City grandees in London to say she "will not compromise" on what people had voted for in the 2016 referendum.

She said Britons "overwhelmingly" wanted her to "get on" with leaving the EU at the address on Monday night.

Her comments made to the annual Lord Mayor's Banquet seemed to extinguish hopes that the Cabinet might sign off a deal when it meets on Tuesday.

If no deal is agreed by Wednesday, the prospect of a special Brexit summit in November will recede sharply, further reducing Mrs May's chances of getting a vote in Parliament before Christmas.

Mrs May told the audience at the Guildhall in London that while both sides wanted to achieve a viable Withdrawal Agreement, "what we are negotiating is immensely difficult".

She added: "Overwhelmingly, the British people want us to get on with delivering Brexit, and I am determined to deliver for them.

"I want them to know that I will not compromise on what people voted for in the referendum.

"This will not be an agreement at any cost."

She repeated her assertion that a deal must give the UK control of "our laws, borders and money", plus the freedom to strike trade deals while protecting jobs, security and the Union.

Both the EU and UK sides had earlier said issues remain to be settled despite weekend talks that went on into the early hours of Monday morning.

Downing Street said that reports that Brussels' chief negotiator Michel Barnier expected the "parameters" of a deal to be presented to ministers for approval at their regular weekly meeting should be taken "with a bucket of salt".

It is not thought that any deal will be on the table at the Cabinet meeting in 10 Downing Street, which will instead hear an update on negotiations and discuss preparations for a possible no-deal withdrawal from the EU.

The Prime Minister's official spokesman rejected suggestions that Wednesday represents a hard deadline to arrange a summit, repeating Mrs May's position that she wants a deal "as soon as possible" but that it "can't be at any cost".

Meanwhile, one Brexit-backing Cabinet minister cautioned that the Prime Minister would not have a free hand in pushing her plans through.

International Development Secretary Penny Mordaunt told Sky News: "The important thing is that there are two checks on this deal - there is Cabinet and there is Parliament.

"Cabinet's job is to put something to Parliament that is going to deliver on the referendum result."

Officials from both sides were engaged in talks in Brussels which began on Sunday and lasted until 2.45am on Monday but failed to produce a decisive breakthrough.

Mr Barnier told ministers from the 27 remaining EU nations at a meeting of the general affairs council that key issues remained unresolved.

"Michel Barnier explained that intense negotiating efforts continue, but an agreement has not been reached yet," said an official statement.

"Some key issues remain under discussion, in particular a solution to avoid a hard border between Ireland and Northern Ireland."

A witness to the meeting told the Financial Times that the chief negotiator had told the EU27 ministers that "the parameters of a possible agreement are very largely defined" and that the UK Cabinet would meet to examine them on Tuesday.

But ministers emerging from the meeting did little to encourage expectations of an early resolution.

Ireland's deputy prime minister Simon Coveney told reporters in Brussels said there was "still clearly work to do" to reach an agreement.

And a senior Brussels source said that work was "ongoing", adding: "We're not there yet."

The lack of decisive progress in Brussels came as further details emerged of reported reservations voiced about Mrs May's strategy by senior ministers at the crunch Chequers meeting in July.

Home Secretary Sajid Javid, Defence Secretary Gavin Williamson and Chancellor Philip Hammond were among Remain-supporting ministers who raised concerns about the Chequers plan, the BBC reported.

Mr Javid described the proposal for a common rule book with the EU for goods and agriculture as "very worrying", while Mr Hammond questioned whether the 27 other countries in the union would accept such a plan, the broadcaster said.