"It is shameful that the European Union have allowed Spain an effective veto over the future of British sovereign territory, flying in the face of the will of the people of Gibraltar".
Papers setting out the EU's Brexit talks strategy say that the region will only be included in a post-Brexit trade deal if Spain agrees with the terms.
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.
Mr Brake said: "Confirmation that Gibraltar's future must be agreed by the United Kingdom and Spain shows just how damaging the Government's hard Brexit will be on this strategically-important British territory".
Gibraltar's chief minister has told Sky News the territory "is not going to be a political pawn in Brexit" and will become even more British after leaving the union.
Still, sensing an opportunity after the outcome, Spain again proposed shared sovereignty, arguing it would allow Gibraltar - whose economy largely depends on the European Union single market - to remain in the bloc.
Spanish Foreign Minister Alfonso Dastis told the national parliament on Wednesday that Madrid would oppose extending EU-UK trade arrangements to Gibraltar to protect its economic interests in the area.
China's man-made S.China Sea islands nearly complete
Duterte repeated that he would not go to war with militarily superior China over the territorial conflict. However, Beijing has defended its actions saying its military equipment will add to the region's safety.
The residents, who are British citizens, voted 96% Remain in the June referendum.
The clause was included in the negotiating strategy set out by the European Council on Friday, which also said that the United Kingdom must settle its Brexit bill and agree the future of EU citizens in the United Kingdom before trade deal talks could start.
Spain's conservative government, which has been particularly vocal about getting Gibraltar back, welcomed the latest development.
This detail is key as it means Prime Minister Theresa May and acting Spanish Prime Minister Mariano Rajoy may have to hold bilateral discussions over the territory if any points of contention arise during Brexit negotiations.
The Tory chairman of the all-party parliamentary group on Gibraltar, Jack Lopresti, accused Spain of using Brexit as "a fig leaf for trouble-making over the status of Gibraltar".
Liberal Democrat foreign affairs spokesman Tom Brake said: "Theresa May must urgently produce a plan that protects the citizens of Gibraltar, including their businesses and communities".
Beside Gibraltar, the Council guidelines include other United Kingdom border issues affected by Brexit, including between Nothern Ireland and the Republic of Ireland, where "flexible and imaginative solutions will be required", to avoid a hard border, the text says.