Theresa May has offered reassurance to the people of Gibraltar that the UK remains "steadfastly committed" to the Rock amid concerns over the Brexit process.

The issue of Gibraltar was raised in the draft EU negotiating guidelines circulated by European Council president Donald Tusk, which indicated Madrid would be given a veto over the Rock's participation in a future deal.

The Prime Minister spoke to Gibraltar's leader Fabian Picardo to tell him the UK remained "absolutely dedicated to working with Gibraltar for the best possible outcome on Brexit".

A Downing Street spokeswoman said Mrs May "reiterated our long-standing position that the UK remains steadfastly committed to our support for Gibraltar, its people and its economy".

She went on: "The Prime Minister said we will never enter into arrangements under which the people of Gibraltar would pass under the sovereignty of another state against their freely and democratically expressed wishes, nor will we ever enter into a process of sovereignty negotiations with which Gibraltar is not content.

"The Prime Minister said we remain absolutely dedicated to working with Gibraltar for the best possible outcome on Brexit and will continue to involve them fully in the process."

Mrs May’s reassurance on the Rock’s future came after Sir Michael Fallon, the Defence Secretary, vowed to protect Gibraltar "all the way" during the Brexit process while Lord Howard, the former Conservative leader, suggested the PM could even be prepared to go to war to defend the British overseas territory.

Mr Picardo has insisted that any future UK-EU trade deal must apply to Gibraltar.

Spain has a long-standing territorial claim on Gibraltar, which has been held by the UK since 1713 and has the status of a British overseas territory.

The issue was not mentioned in the PM’s Article 50 letter but Sir Michael told BBC One's Andrew Marr Show: "Gibraltar is going to be protected all the way because the sovereignty of Gibraltar cannot be changed without the agreement of the people of Gibraltar and they have made it very clear they do not want to live under Spanish rule.

"It is interesting in the draft guidelines from the EU that Spain is not saying that the whole thing is subject to the transfer of sovereignty."

Mr Picardo has lobbied ministers to ensure its interests are represented and said the issue was referred to "tangentially" in Mrs May's letter, which referenced the Government's white paper on Brexit.

He told the Andrew Marr Show: "I'm not thrilled that we are in the situation in which we are - Gibraltar voted 96 per cent to remain.

"But we have energetically and enthusiastically decided that we have to support the Prime Minister in this process of making Brexit a success for Britain and for Gibraltar.

"Therein lies the rub. When we get the deal on Brexit, it must be a deal that applies across the United Kingdom in respect of future trade and if there is such a deal, it is only fair, proper and right that it should also apply to Gibraltar."

After speaking to Mrs May "at length", he said she was "very supportive".

Lord Howard said there was "no question" about the UK's stance on the sovereignty of Gibraltar, comparing the Rock to the Falkland Islands.

He told Sky News' Sophy Ridge on Sunday: "Thirty-five years ago this week, another woman prime minister sent a taskforce halfway across the world to defend the freedom of another small group of British people against another Spanish-speaking country, and I'm absolutely certain that our current prime minister will show the same resolve in standing by the people of Gibraltar."

Meantime, Tim Farron, the Liberal Democrat leader, said: "It is unbelievable that within a week of triggering Article 50 there are Conservatives already discussing potential wars with our European neighbours.

"In only a few days the Conservative right are turning long-term allies into potential enemies. I hope this isn't a sign of the Government's approach to the long negotiations to come

"Brexiteers have gone from cheering to sabre rattling for war in four days, it is absolutely ludicrous," added the Cumbrian MP.