British Prime Minister Theresa May has said that regulatory differences already exist between Northern Ireland and Britain, which have not challenged the constitutional integrity of the UK.

Speaking during a visit to Belfast, Mrs May said she has had discussions with Taoiseach Leo Varadkar on how to build on the significant improvement in relations between the UK and Ireland in recent years.

She also said she hopes that when MPs vote on the Brexit deal reached between the UK and the European Union, they will think of the national interest.

Mrs May faces a battle to get the draft agreement through a House of Commons vote on 11 December.

The DUP's ten MPs, which are propping up her government, have pledged to oppose the agreement.

The backstop agreement is an issue which the DUP party opposes.

The party's leader Arlene Foster has already said that if Mrs May wants its continued support, it means removing the Irish backstop from the withdrawal deal.

The backstop is designed to avoid a hard border on the island of Ireland post-Brexit.

Mrs May said the Brexit deal delivers on the key issues - such as ending free movement and the jurisdiction of the European Court of Justice - while also protecting British jobs, security and the UK itself.

"People don't want to go back to uncertainty and division, which is what would happen if people don't support this deal," she said.

"MPs will need to think about the people they represent and the impact on their constituents.

"It is a good deal from the UK, a good deal for Northern Ireland and a good deal for all of the UK," she added.

Regulatory differences already exists between NI and the UK, says British PM | https://t.co/oUmlfh3Uz3 pic.twitter.com/ioVL5v1784 — RTÉ News (@rtenews) November 27, 2018

Earlier, Mrs May rejected claims by Mrs Foster that she has "given up" on getting a better Brexit deal.

In an interview with the BBC, Mrs Foster said: "The disappointing thing for me is that the Prime Minister has given up and she is saying this is where we are and we just have to accept it.

"She may have given up on further negotiations and trying to find a better deal but I have not given up.

"I believe in a better way forward and I believe we must find that."

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Mrs May's Belfast visit comes as US President Donald Trump last night said the withdrawal treaty could hamper trade deals between the UK and the US - something which Downing Street denied.

Mrs May's Brexit deal has also been attacked as the "worst of all worlds" by one of her staunchest allies.

Former defence secretary Michael Fallon confirmed he will not vote in favour of the agreement when it comes to Parliament, where he said it seems "doomed" to fail.

The MP, who until now had been staunchly loyal, told BBC Radio 4's Today programme: "My fear is that this deal gives us the worst of all worlds, no guarantee of smooth trade in the future and no ability to reduce the tariffs that we need to conclude trade deals with the rest of the world.

"So, unless the House of Commons can be persuaded somehow that those are possible, then I think, yes, the deal is doomed."

Mr Fallon also said the government must heed President Trump's claim last night that the Withdrawal Agreement "sounds like a great deal for the EU".

He said: "It's no use us just brushing that off, saying 'No, no, we can do a deal with America'; he's the President of the United States, and if he says it's going to be difficult, then it certainly looks like it's going to be difficult.

"This is not a good deal and we need a better deal."

Meanwhile Sinn Féin leader Mary McDonald has said her party's seven votes at Westminster "will hardly be the deciding factor" for passing the Brexit deal.

She said it was ridiculous to think that Sinn Féin MPs would go to the House of Commons "on a white charger" and save the Prime Minister.

Speaking on RTÉ's Today with Sean O'Rourke, Deputy McDonald said the reality is that Brexit will happen - whether on Mrs May's watch or under Labour leader Jeremy Corbyn.

Ms McDonald said that Westminster looks after specifically British interests and Sinn Féin's presence there would achieve nothing.

Yesterday, Taoiseach Leo Varadkar said he believed Sinn Féin MPs should take up their seats at Westminster before next month's vote on the proposed Brexit deal.