A United Kingdom government spokesperson explained it meant the British lawmakers would talk directly with Spain over any Gibraltar-specific issues involved in any trade deal.
May's spokeswoman told reporters earlier on Friday: "We've negotiated very openly and constructively with the European Union in matters relating to Gibraltar and worked closely with Spain".
The British government released a letter from the British ambassador to the EU, Tim Barrow, to the head of Tusk's secretariat spelling out that Britain would make no presumption that any future EU-U.K. trade pact would apply to Gibraltar.
Chief Minister of Gibraltar Fabian Picardo criticised Spain's insistence on a written guarantee. But they also heard strong words from Spanish ministers that left them unwilling to call Sanchez's bluff without further talks.
The diplomatic spat which threatened to derail the Brexit process was resolved after emergency talks involving Sanchez, European Council president Donald Tusk and European Commission president Jean-Claude Juncker.
Spain's junior minister for the EU, Luis Marco Aguiriano, said Friday that officials could tweak Article 184 to make it clear that future relations between the EU and Gibraltar "will be negotiated with the United Kingdom with Spain's prior consent".
"For the withdrawal negotiations, given there are some circumstances which are specific to Gibraltar, we held talks with Spain which directly involved the Government of Gibraltar", May's spokesman said.
Mrs May said: "We have ensured that Gibraltar is covered by the whole Withdrawal Agreement and by the implementation period and we will always negotiate on behalf of the whole United Kingdom family, including Gibraltar, and in the future relationship we will stand up for their interests". "A lot of people - not just Brexit, but all kinds of other people, whether it's the Italians or the Greeks or the Hungarians or the Catalans, or whoever it is - are all having big populist movements".
Mrs May also faced domestic difficulties as the Democratic Unionist Party held its conference in Belfast - with Boris Johnson making a guest appearance.
In particular, it states that the article "imposes no obligations regarding the territorial scope of such agreements and that there is, therefore, no obligations or presumption, on the basis of this provision, for such agreements to have the same territorial scope of the one provided in Article 3 of the withdrawal agreement".
Diplomats said there was no doubting the passion behind the Spanish arguments when advisers to the 27 European Union leaders met in Brussels on Friday to prepare the summit: "The Spanish are very proud people and this is absolutely important for them", one participant in the talks told Reuters.
"It's a way of leaving the European Union with minimum negative impact on our economy", he said.
City lobby groups said the issue, which emerged as one of the key Brexit battlegrounds, was being used as a bargaining chip in a "game of high-stakes political poker".
"Parliament will have the chance to do that in a few weeks´ time when it has a meaningful vote on the deal", the prime minister said. We will be faced with potential economic chaos; I am sure we would get a very negative reaction from the business community, from investors, from the markets.
"If this deal doesn't go through, what happens is we end up back at square one", May said.
Throughout the long and complex negotiations that have taken place over the a year ago and a half, I have never lost sight of that duty.
"Don't put the two together, they're quite separate".