A “new sense of optimism” now exists in the Brexit talks, Theresa May will tell MPs today, after David Davis suggested the chances of Britain leaving the European Union without a trade deal had “dropped dramatically” following last week’s agreement.

The Brexit Secretary said he wanted a trade deal that was “Canada plus plus plus,” which would not only cover trade but also services.

However, he warned Brussels Britain would not pay a penny of the estimated £39 billion divorce bill if there was no trade deal with the EU.

Labour and the SNP made clear the UK Government’s commitment to “full alignment” on the Irish border issue meant the country was now heading for a soft Brexit.

Sir Keir Starmer, the Shadow Brexit Secretary, said his party wanted close alignment with the EU post-withdrawal to retain the benefits of the single market and the customs union, which would involve “easy movement” of people with Europe.

Ian Blackford, the Nationalist leader at Westminster, warned a hard Brexit would lead to an “unparalled” economic threat to the economy but argued he believed “ultimately” the UK would decide to stay in the single market and customs union.

This afternoon, the Prime Minister will give a Commons statement on her “Brexit breakthrough” when she is expected to receive a rapturous reception from her Conservative colleagues.

Hours earlier, Mrs May will chair a meeting of Cabinet – brought forward a day because of her attendance at a climate change summit in Paris on Tuesday – when she will explain how she envisages the Government’s approach to phase two of the talks on transition and trade. Next week, senior ministers will for the first time discuss the “end state” to the Brexit negotiations.

Today, the PM is expected to say: "This is not about a hard or a soft Brexit. The arrangements we have agreed to reach the second phase of the talks are entirely consistent with the principles and objectives that I set out in my speeches in Florence and at Lancaster House.

“I know that some doubted we would reach this stage. I have always been clear that this was never going to be an easy process. It has required give and take for the UK and the EU to move forwards together...”

Stressing how “nothing is agreed until everything is agreed,” Mrs May will tell MPs: “But there is a new sense of optimism now in the talks and I fully hope and expect that we will confirm the arrangements I have set out today in the European Council later this week.”

She will say the country can now move on to building the “bold, new economic and security relationships” that will underpin a new deep and special partnership with the EU.

“A partnership between the European Union and a sovereign United Kingdom that has taken control of its borders, money and laws once again. A partnership that is in the best interests of the whole United Kingdom and a partnership which can deliver prosperity and security for all our people, for generations to come," the PM will add.

Mr Davis said the chances of Britain leaving the EU without a trade deal had now "dropped dramatically” but he warned if a no-deal scenario happened, then the divorce settlement, calculated at somewhere between £35bn and £39bn, would not be paid.

Asked about comments by Chancellor Philip Hammond, who last week suggested it would be "inconceivable" for the UK to fail to honour its international obligations, the Brexit Secretary told the BBC’s Andrew Marr Show: "No. It is conditional on an outcome. I am afraid that wasn't quite right.”

He went on: “It is conditional on getting an implementation period; conditional on a trade outcome. No deal means that we won't be paying the money."

But Labour made clear, if in power, it would pay over money to Brussels even if there were not a trade deal.

Rebecca Long-Bailey, the Shadow Business Secretary, said: “Our position is different; we appreciate we've got to honour our legal obligations and that sets our position of trust across the world to make trade deals with relevant countries…If you had a mortgage, you'd still be expected to pay the sums that you would need to honour...”

But she also told John Pienaar on Five Live: “We need to stop talking about no deal because that is not a viable option.”

Earlier her colleague, Sir Keir agreed that, while freedom of movement would end with Brexit, “easy movement” of people in both directions across the continent would continue but would have to be negotiated.

Meanwhile, a spat opened up between Dublin and London after Mr Davis suggested the UK’s agreement to “full alignment” on the Irish border was “much more a statement of intent than it was a legally enforceable thing."

Joe McHugh, the Irish Government’s Chief Whip branded the Secretary of State’s comments "bizarre" and insisted: “We will, as a sovereign government in Ireland, be holding the United Kingdom to account as will the European Union…This, as far as we're concerned, is a binding agreement, an agreement in principle."