The EU will not back down in its support for Spain’s demands when it comes to the Rock of Gibraltar in Brexit negotiations, senior European diplomats have said. The European council, whose members comprise the EU member states, shocked Downing Street by saying the British overseas territory could be included in a trade deal between London and Brussels only with Spain’s agreement.

Early on Sunday, a former Conservative leader waded into the row by claiming that Theresa May would be prepared to go to war to protect the territory as Margaret Thatcher once did for the Falklands. In comments that were immediately criticised by Labour and the Lib Dems as inflammatory, Michael Howard said there was “no question” of Britain weakening its stance with regards to the sovereignty of one of its overseas territories.

“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,” Howard told Sophy Ridge on Sunday on Sky News.

Downing Street refused to comment on the Tory peer’s intervention, but revealed that May had called Fabian Picardo, the chief minister of Gibraltar, on Sunday morning to say the UK remained “steadfastly committed to our support for Gibraltar, its people and its economy”.

A short guide to Gibraltar Ever since the Anglo-Dutch fleet captured Gibraltar 313 years ago during the war of Spanish succession, the small territory at the southern tip of Spain has been a bone of contention between Madrid and London. Although British sovereignty was formalised by the treaty of Utrecht in 1713 and Gibraltar became a British colony in 1830, Spain has always bristled at the idea of UK ownership. Two referendums - in 1967 and 2002 - have shown that the overwhelming majority of residents wish Gibraltar to remain British. Despite accusations of double standards given its two enclaves in north Africa, Spain has refused to relinquish its claim.

The prime minister added that the British government would “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”, Downing Street said.

Picardo had himself flown to London for an interview on the Andrew Marr show in which he echoed comments made privately by British officials. He suggested that the demand in the European Council’s draft negotiating guidelines could be watered down before the 27 member states formally adopt them at the end of the month. “That’s just a draft at the moment. Let’s see what comes back on 29 April,” he said.

However, senior EU diplomats, talking to the Guardian, have dismissed the suggestion that the EU will go soft on the issue of Gibraltar in the coming weeks, and warned that Spain had spent time and effort in cultivating support among the other 26 member states on the position.

“Spain are taking this very, very seriously,” one diplomat said. “I think there is support across the board among the member states. Why not?

“It is not a problem that was born yesterday. It has been with us a long time and we have always listened to both sides. Now we are going to support the member state. That is the philosophy behind it. I wouldn’t think any of the 26 other states will somehow try to undermine this clause.”

They expressed surprise that the prime minister had not mentioned the future of Gibraltar in her six-page letter notifying the EU of the UK’s intention to leave the union, delivered to the European Council’s president, Donald Tusk, on Wednesday.

“I was personally surprised,” said one diplomat. “But if Theresa May thinks the status of Gibraltar and its border with Spain is of little significance, the EU does not.”

Picardo insisted that his administration had worked closely with the prime minister on the article 50 notification letter, and stressed that the people of Gibraltar had expressed their views to remain British, democratically, claiming that co-sovereignty would drastically change who they were as a nation.

He also insisted he was assured Britain would never allow Gibraltar to fall out of a trade deal agreed by the EU and the UK. “Therein lies the rub,” he said. “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.”

Speaking on the same programme, the defence secretary, Michael Fallon, stressed that the letter referred to the government’s Brexit white paper, which had repeatedly referred to the question of Gibraltar. “We’re going to look after Gibraltar. Gibraltar is going to be protected all the way because the sovereignty cannot be changed without the agreement of the people of Gibraltar,” he said.

Although the question of Gibraltar had been included in the EU’s draft negotiating guidelines, circulated on Friday, Fallon attempted to ratchet down the controversy by stressing that Spain had not specifically raised any issue of sovereignty.

Spain has long sought co-sovereignty of Gibraltar, but the current push for a say in the future of the territory may have more to do with a desire to torpedo the current super-low corporate tax rate that makes the rock attractive to the financial services sector.

Spain also argues that Gibraltar’s airport is illegally located. It says the 1713 Treaty of Utrecht, which ceded the castle, port and town of Gibraltar to Britain, did not include the rights to the isthmus on which the landing strip is built.

On Saturday, Spain said it would not veto an attempt by an independent Scotland to join the EU, in a boost to Nicola Sturgeon’s campaign for a second independence referendum and the clearest sign yet that Brexit has softened Madrid’s longstanding opposition. Alfonso Dastis, the Spanish foreign minister, made it clear that the government would not block an independent Scotland’s EU hopes, although he stressed that Madrid would not welcome the disintegration of the UK.