HOPES are continuing to rise at Westminster that cross-party talks on Brexit can produce a breakthrough deal next week as Andrea Leadsom, the Commons Leader, told MPs she hoped they would “come to fruition very soon”.

The expectation is that the next plenary session of the talks involving Cabinet ministers and their Labour shadows will take place on Tuesday. If a deal is struck, then Theresa May is likely to chair a special Cabinet on Wednesday before making a Commons statement.

Ruth Davidson, speaking ahead of her return to frontline politics this weekend following her maternity leave, was encouraged by the mood music coming out of Whitehall, saying it could mean there would be a breakthrough soon.

“I really want to see it because we know more than anyone in Scotland that sometimes the divisions after referenda are bigger than the divisions before and we've got into really entrenched positions,” the Scottish Conservative leader told STV.

"My view through all of this is that we're going to have to meet somewhere in the middle between the people who want to overturn the referendum and re-run it and those who want a no-deal Brexit."

Stressing how there had to be a willingness to move on both sides, Ms Davidson acknowledged: “To get a deal through the Commons, there will need to be ground given."

During Business Questions in the Commons, Ms Leadsom referred to the cross-party talks, telling MPs: "We all hope they come to fruition very soon and we make some progress in delivering on Brexit, which the House has committed itself to doing but has failed singularly to achieve so far."

Any compromise deal would lead to splits within Conservative and Labour ranks.

Earlier this week at Cabinet, Michael Gove warned colleagues that they might have to offer concessions so the Labour leader could claim victory in the talks and sell the deal to his MPs.

The Environment Secretary, one of the leaders of the Leave campaign in the 2016 referendum, argued it would be better to accept the "unpalatable" outcome of a deal with Labour than the "disastrous" outcome of Brexit not happening at all.

Julian Smith, the Chief Whip, was equally frank, saying it was “time to get real” over the options before them.

The focal point appears to be on the issue of customs; Labour wants a full and permanent customs union with the EU while the Government wants a customs arrangement, so that Britain can do future trade deals.

The suggestion is that the two sides, as Ms Davidson alluded to, would meet halfway.

The Con-Lab deal would refer to a “customs arrangement” but this would include Britain aligning all tariffs on goods with the EU and so Brussels would negotiate trade deals on Britain’s behalf.

However, it is thought there might be some limited scope for the UK to do deals on services like banking and insurance.

On Wednesday, the Prime Minister, when asked about a customs compromise, told MPs it "depends what your definition of a customs union is”.

In order to get the Government’s Withdrawal Agreement Bill[WAB] through the Commons to ratify the Brexit deal, the parliamentary arithmetic has to be right.

As has been seen, there is no majority for any proposal; so Mrs May, to try to avoid new British MEPs taking their seats, will have to get a deal soon to enable the legislation to pass by June 30, the date when MEPs formally take their seats.

Given it will take some weeks to process WAB through the Commons and Lords, time is of the essence and so next week looks crucial.

But a soft Brexit compromise, enabling the PM to get a deal through, will mean her winning over the bulk of Labour MPs but alienating a quarter of her own party. A customs compromise that will not enable Britain to do its own full trade deals will lead to resignations, most likely to include that of Liam Fox, the International Trade Secretary.