Nevertheless, the EU's proposal to give Spain the power to veto any Brexit deal that applies to the British territory represents a major diplomatic victory.
Last year, Spain formally presented Britain with a proposal for joint sovereignty of Gibraltar - an offer that nearly everyone on the British overseas territory rejected.
Gibraltar has a population of around 32,000 and 96 per cent of the residents who voted in the Brexit referendum voted to remain in the EU.
A Brexit deal will not automatically apply to Gibraltar and could be vetoed by Spain, according to the EU's draft guidelines for the UK's exit negotiations, reported the Independent on Friday.
The council's stance on the British enclave off southern Spain, however, has angered Gibraltar's chief minister Fabian Picardo who said the potential veto was "unacceptable".
Insisting that the guidelines would allow Spain "to discriminate against the British people of Gibraltar", he said: "Gibraltar is not going to be a political pawn in Brexit, neither is it going to be a victim of Brexit".
The draft proposal means that Madrid could potentially block Gibraltar's access to any trade deal Britain negotiates with the European Union, opposition politicians in the Rock claim.
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Mr Picardo added: "What we are seeing is a clear manifestation of the predictably predatory attitude that we anticipated Spain would seek to abusively impose on its partners, as they have been threatening to do since the referendum took place and as the only member of the European Union with an obsession with Gibraltar".
Unless Theresa May is prepared to sacrifice the future of Gibraltar's 30,000 inhabitants to secure a good deal for the rest of the United Kingdom then she could have to make concessions to Spain.
Downing Street said Mrs May had made clear the Government was "absolutely steadfast in our support of Gibraltar, its people and its economy" in the House of Commons on Wednesday.
Spanish politicians picked up on the fact that Theresa May's Article 50 letter, which triggered the two-year Brexit process, did not mention Gibraltar, while it did mention the land border between Northern Ireland and the Republic of Ireland.
Though Gibraltar residents voted overwhelmingly in favor of remaining in the European Union, the inhabitants of the rock want to stay under United Kingdom jurisdiction. The whole world and the whole European Union should know: "this changes nothing in respect of our continued, exclusive British Sovereignty".
"It's predictable that, given Spain's previous behavior, they would try and use Brexit as a fig leaf for trouble-making over the status of Gibraltar", Lopresti said Friday. For people living in Gibraltar the outcome of the negotiations may have significant, and life-changing, consequences.