The latest spat arose from the EU's Brexit negotiating guidelines which leave Britain and Spain to thrash out what agreements will apply to Gibraltar.
A spokesman for the Gibraltar government told The Telegraph: "Today's illegal incursion by a Spanish naval vessel is a timely demonstration of the way in which Spain routinely conducts itself in breach of the UN Convention on the Law of the Sea".
On 3 April, May laughed off suggestions of a war with Spain, saying: "What we are doing, with all European Union countries in the European Union is sitting down and talking to them".
London and Madrid have had a long and bitter dispute over the huge rock off Spain's southern coast, which has been a British territory for more than 300 years.
Michael Howard, a former Tory leader and now a member of the House of Lords, said that the tussle over Gibraltar evoked the UK's war with Argentina in the South Atlantic over the Falkland Islands in 1982. Her office also confimed she had spoken to Fabien Picard, chief minister of Gibraltar, to assure him that the territory's status is not up for renegotiation.
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"Spain is going to jump at this opportunity to try and take advantage of the situation but when it comes to the crunch I think we've got to take one step at a time and not overreact, be calm", said firefighter Liam Byrne, speaking in a street on the peninsula.
After an European Union document suggested that Spain would be given a say on post-Brexit agreements governing the Rock, Tory peer Lord Howard said he was certain that the Prime Minister would be ready to defend the Rock as Margaret Thatcher did the Falklands.
A spokesman said on Monday: "All that Lord Howard was trying to establish is the resolve that we will have to protect the rights of Gibraltar and its sovereignty".
Cawdery said: "In my opinion, there is absolutely no chance of any degree of Spanish sovereignty over Gibraltar within any reasonable timeframe-given this, talk of the potential for such in some areas of the United Kingdom press seems misguided".
Currently, there are 32,000 people living on the minuscule seven square kilometer territory ceded to the United Kingdom in 1713 and still claimed by Spain.