The British Prime Minister Theresa May has repeatedly refused to state whether she would quit if Westminster MPs fail to back her Brexit deal.

Continuing a public relations offensive in an attempt to sell her agreement with the EU, Mrs May dodged questions about her own personal future if the House of Commons does not support her.

She will head to an EU summit in Brussels this weekend as she bids to secure a sign off from the bloc's 27 other leaders on the terms of Britain's divorce.

Spain has raised a last-minute obstacle by vowing to "veto Brexit" over the issue of Gibraltar - with Madrid asking for a written UK promise on the peninsula before Sunday's summit.

No single state can block the deal, as under EU rules the withdrawal treaty will be adopted by a qualified majority rather than a unanimous vote.

However, a no vote from Spain - one of the largest states in the union - would cast a cloud over the vote as EU leaders work to maintain a united front on Brexit.

While Tánaiste Simon Coveney has said there may be some room for manoeuvre in the agreement.

"I think you will see Britain and Spain working with Michel Barnier and his team - and indeed other European leaders - to find a resolution to this," he said.

Mrs May is also facing a headache at home with UK Labour, the DUP, the SNP, Liberal Democrats and close to 90 of even her own MPs opposed to her agreement.

It means Mrs May is facing a prospect of the House Commons rejecting her Brexit deal when MPs hold a "meaningful vote" on the agreement - expected to be held next month - unless she can persuade a sizeable number of parliamentarians to reverse their position.

"I'm not thinking about me"

Speaking on BBC Radio 5 Live, Mrs May would not say whether she would resign or not if MPs fail to back the agreement.

"I'm focused on actually ensuring we do get this deal through parliament because I believe this is absolutely the right deal for the UK," she said.

Asked twice more if she would quit if parliament rejects her deal, Mrs May added: "As I'm sitting here, I'm not thinking about me.

"I'm thinking about getting a deal through that delivers on the people of this country.

"That's what drives me and that is what is at the forefront of my mind.

"And when I say I'm going to be focused over the next few weeks until the meaningful vote in parliament at getting that vote through, yes I will.

"I'm going to be doing other things too, I'm going to be around the country, I'm going to be explaining the deal to people up and down the country because I think this is important.

"It's not just about the MPs in Westminster looking at the deal, it's about people across the country understanding what the deal is about. So, that's my focus."

She also attempted to clarify whether MPs rejecting her deal would prompt a "no-deal" Brexit - or even the UK remaining in the EU.

"From my point of view, personally, there is no question of no Brexit because the government needs to deliver on what people voted for in the referendum in 2016," Mrs May told the BBC.

"So, as far as I'm concerned, the UK is leaving the EU on March 29th 2019.

"But people will have heard, if they've look at what's happened in parliament, they'll have heard there are voices in parliament that actually want to frustrate Brexit and want to stop Brexit."

Fox: Backstop could hamper trade deals

Most of the criticism of the Brexit agreement has focused on the backstop to avoid a hard Irish border.

British Trade Secretary Liam Fox claimed, if the UK were to fall into the backstop in the absence of an agreement on the future EU-UK relationship, it could hamper the country's ability to secure independent trade deals with non-EU countries.

"If we were in the backstop, it would be quite difficult for us to engage with partners, not knowing when the end date would be when we could implement any agreement," he said on a trip to Northern Ireland.

"And so our aim is that we would never get to the backstop."