Former British Conservative leader Michael Howard has suggested the UK would go to war to defend the sovereignty of Gibraltar, a UK-controlled territory at the southern tip of Spain.
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.
European Council president Donald Tusk has suggested Spain be given a veto over Gibraltar's future under the Brexit process, which could see its control passed to Madrid.
Last week UK Prime Minister Theresa May triggered the formal process of quitting the European Union after a referendum last year indicated the majority of respondents supported Brexit.
Lord Howard said Mrs May would show the same "resolve" as Margaret Thatcher did when she went to war with Argentina over control of the Falkland Islands in 1982.
An estimated 655 Argentine and 255 British servicemen lost their lives in the Falklands conflict.
The Liberal Democrats said he was "sabre-rattling" and Labour also criticised the "inflammatory" remarks.
Mrs May said the UK was "steadfastly committed" to Gibraltar, after the EU raised it ahead of Brexit talks.
Lord Howard said that 35 years ago, "another woman Prime Minister sent a taskforce halfway across the world to protect another small group of British people against another Spanish-speaking country".
"And I'm absolutely clear that our current woman Prime Minister will show the same resolve in relation to Gibraltar as her predecessor did," he said.
Labour's shadow foreign secretary Emily Thornberry said the "inflammatory" comments would not help Britain get what it needed from Brexit negotiations."
Liberal Democrat leader Tim Farron said in only a few days the Conservative right were 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."
Defence Secretary Sir Michael Fallon said the UK would protect Gibraltar "all the way" because its residents had "made it very clear they do not want to live under Spanish rule".
After Mrs May spoke to Gibraltar's chief minister Fabian Picardo on Sunday, a Downing Street statement said: "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."
Mr Picardo said he was "energetically and enthusiastically" supporting Mrs May in her Brexit negotiations.