e Minister Theresa May vowed on Sunday that she will not allow Gibraltar fall from British control as the issue took precedence in the Brexit row.
Gibraltar is home to around 33,000 people, with an offshore finance sector and a key online gambling industry that operates with the rest of Europe.
May's remarks came as Spain promised it would not close its border British overseas territory post-Brexit. She told Chief Minister of Gibraltar Fabian Picardo that she would never "enter into a process of sovereignty negotiations with which Gibraltar is not content."
However, Spain said on Sunday that it had zero post-Brexit plans to close its border with the territory, as it depends on the crossing for visitor flow and supplies.
The EU has made clear that Spain will have to agree to lengthen any trade deal between the bloc and Britain to cover Gibraltar, meaning that Gibraltar's access to any deal could possibly be blocked by Madrid.
Politicians on the 6.7-square-kilometre (2.6-square-mile) peninsula on the southern tip of Spain, are apprehensive of Madrid using the veto to seek sovereignty over "the Rock".
May explained to Picardo that "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," according to a transcript of the phone call released by Downing Street.
"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."
"The UK remains steadfastly committed to our support for Gibraltar, its people and its economy," it said. A third of Gibraltar’s population makes the crossing daily to work from the Spanish-controlled region Campo de Gibraltar, which surrounds Gibraltar. They fear that Madrid may make things tougher at the border.
Alfonso Dastis, the Spanish Foreign Minister said "There is no intention to close the border. The idea is that Spaniards who live in the Campo de Gibraltar and who work in Gibraltar continue to do so," in an interview published in Spain's daily newspaper El Pais.
"This is a disgraceful attempt by Spain to manipulate the European Council for its own, narrow, political interests," Picardo said in a statement.
On Friday, Picardo hit out at the EU proposal of a trade deal, branding it "unnecessary" and "discriminatory."
Foreign Minister Boris Johnson wrote in the Sunday Telegraph, "Gibraltar is not for sale. Gibraltar cannot be traded. Gibraltar will not be bargained away.
"The status of Gibraltar has been unchanged since 1713. It made no difference when the UK joined the Common Market in 1973 and when Spain was not yet a member. It should make no difference today."
Johnson added that the policy of the government "remains fixed and firm. The sovereignty of Gibraltar cannot be changed without the express consent of the UK and the people of Gibraltar."
This was demonstrated in 2002, when almost 99% of Gibraltarians chose to stay British, rejecting a referendum on shared sovereignty with Spain.