THERESA May has to accept that the only way she will get a Brexit deal through Parliament is to back Labour's five demands, shadow chancellor John McDonnell has said.

He told BBC Radio 4's Today programme his party's plans are a "traditional British compromise", and said: "We believe a deal like this, put before Parliament again, could secure a majority and what you're seeing here is, yes, Parliament asserting control, and the Prime Minister has to accept that the only way she'll get something through Parliament is a compromise like this."

He added a second referendum is still on the table if May does not approve the suggested deal or Parliament cannot reach an agreement.

McDonnell said Labour's deal would command a "secure" majority.

He said: "If Theresa May said 'I'll sign up to Labour's deal' and we went to Parliament, I think we would have a secure parliamentary majority.

"But we're at that stage now where we're saying very clearly to everybody that people have looked over the edge of a no-deal Brexit and it could be catastrophic for our economy."

The shadow chancellor added: "In the national interest we have got to come together to secure a compromise, and then if we can't do that, well yes, we have to go back to the people."

Taoiseach Leo Varadkar has arrived in south Belfast ahead of scheduled meetings with Stormont's five main parties.

Labour former minister Chris Leslie has said his "patience is wearing pretty thin" with his party's Brexit policy.

He told BBC Radio 4's World At One: "I have to be honest, my patience is wearing pretty thin with the Labour Party policy on Brexit.

"This is the big issue of the moment and it's going to affect not just trading relationships but percolate right through to the revenues that we have for our public services.

"If I want to avoid another decade of austerity I can't help but focus on what is happening on Brexit, and what is the Labour Party's policy on Brexit, and that is why ... I've got some serious worries about where the leadership are going having basically dropped all of that Labour Party conference policy commitment from September and apparently trying to airbrush the concept of a public vote, letting the public have the final say on this, from where we stand."

In a tweet, EU chief Brexit negotiator Michel Barnier said: "I am looking forward to meeting Steve Barclay in Brussels on Monday evening.

"I will listen to how the UK sees the way through. The EU will not reopen the Withdrawal Agreement. But I will reaffirm our openness to rework the Political Declaration in full respect of European Council guidelines."

Former taoiseach Bertie Ahern has suggested that a border poll on a united Ireland could be called.

He told the BBC: "I wouldn't say inevitable, but I do think you will see a border poll.

"I do think if the UK, which seems almost positive now, pull out of the EU, the issue then will not just be about whether there should be a united Ireland, people will also be reflecting do Northern Ireland want to be in the European Union or not?

"Now, Scotland might have a similar position in years to come.

"But I do see that being a factor that people who want to be in Europe will say a united Ireland is more attractive."

Taoiseach Leo Varadkar has insisted his dinner with the prime minister will not involve any negotiation on the terms of the Brexit deal.

"It's an opportunity for us to meet again to share perspectives on Brexit but, of course, not to engage in negotiations, as they can only be between the European Union and the United Kingdom," he said.

Varadkar was speaking in Belfast ahead of meetings with the five Stormont parties. He will later travel back to Dublin to host Mrs May at Farmleigh House.

"Today is not a day for negotiations, today is a day for us to share our perspectives and for us to listen to each other," he said.

"Negotiations on Brexit only happen between the European Union and the United Kingdom, Ireland being part of the European Union negotiating team of course.

"I think everybody wants to avoid no deal, everybody wants to avoid a hard border and everybody wants to continue to have a very close political and economic relationship between Britain and Ireland no matter want happens.

"There is much more that unites us than divides us and time is running short and we need to get to an agreement really as soon as possible, and I'll be working very hard and redoubling my efforts, along with government, to do that."

Varadkar played down the significance of a meeting on Friday morning between UK Attorney General Geoffrey Cox and his Irish counterpart Seamus Woulfe.

He highlighted that UK and Irish cabinet counterparts meet on regular occasions.

"We are keeping in close contact with the British Government, not just at prime ministerial level but at all levels," he said.

He rejected the suggestion the meeting with May would be a waste of time.

"I believe ultimately we are going to have to get this deal over the line and I am determined to do that and I think any engagement with the British Prime Minister and her team is useful and we will be talking about Brexit and how we move forward and get the Withdrawal Agreement ratified and we will also be talking about Northern Ireland and what we might be able to do in the months ahead to restore the institutions and have them functioning here in Northern Ireland, which is what the people of Northern Ireland want," he said.

The Taoiseach was asked to comment on a Sky News poll that suggested 79% of Irish people were behind his Government's stance on insisting on the border backstop.

"I think that poll is very encouraging, it's good to know that the Irish people are very much behind the position the Government has taken in relation to Brexit and in relation to the Withdrawal Agreement and the backstop," he said.

Varadkar again insisted the backstop was not up for renegotiation.

"But we can talk about the joint political declaration and what changes might be made to that and what assurances may be given that would assist this agreement being ratified," he added.

On the prospect of a no deal, the Irish premier said: "The European Union and Ireland, we are not threatening no deal, we never have. The deadline set on March 29th is one set by the British Government in Britain and it is one that is open to them if they choose to revoke Article 50 or seek an extension to it. Nobody in the European Union, nobody in Ireland is threatening a no deal."

Varadkar was asked to comment on the Labour Party's proposal for Brexit, which include a permanent customs union.

"I have seen them and I think what Jeremy Corbyn has done is fleshed out a potential future relationship which is one that would mean a future relationship that is very close between the European Union and the United Kingdom and I think in that regard they are very interesting," he said.

"But ultimately when dealing with these matters I deal with the democratically elected government of the United Kingdom and that is headed by Prime Minister May."

Varadkar also appeared to defend Donald Tusk when asked about the European Council president's s controversial remarks about a "place in hell being reserved for Brexiteers who advocated leaving the EU without a plan to safely deliver it.

"I don't think people should forget about some of the political rhetoric that has been directed at the European Union," he said "It was only a few months ago that people in the UK Government were comparing the European Union to communism and bear in mind President Tusk – Donald Tusk – spent much of his life fighting to over throw communism.

"So I think there has been a lot of rhetoric coming from a lot of different quarters and I think the best thing to do is just to rise above it."