Prime Minister Theresa May has spoken to Gibraltar's leader, Fabian Picardo, to reassure him the United Kingdom remains "absolutely dedicated to working with Gibraltar for the best possible outcome on Brexit".
Britain is annoyed with Spain and the European Union because the European Union has said Spain should have veto rights on any agreements regarding Gibraltar during the negotiations on Britain's exit from the EU.
Michael Howard, a former Conservative leader, said Sunday that Prime Minister Margaret Thatcher had sent British warships to the South Atlantic in 1982 "to protect another small group of British people against another Spanish-speaking country".
Spain has long disputed British sovereignty over the land, which has been held by the United Kingdom since 1713 and now has the status of a British overseas territory.
But Mr Weston said the row, as Brexit talks loom, was a "storm in a teacup".
Spain dealt Britain another setback Monday by suggesting it would not veto any effort by an independent Scotland to join the European Union, raising the possibility Britain could split after Brexit.
In response to the strong reactions, Spain's Foreign Minister Alfonso Dastis said his government "is a little surprised by the tone of comments coming out of Britain, a country known for its composure".
Mr Picardo has insisted that any future UK-EU trade deal must apply to Gibraltar.
What does Spain say - and Gibraltarians?
At the Downing Street lobby briefing on Monday morning, the prime minister's spokesman ruled out sending a Falklands-style taskforce to protect Gibraltar. He told the Andrew Marr Show: "I'm not thrilled that we are in the situation in which we are - Gibraltar voted 96% to remain".
The EU's negotiating draft negotiating guidelines for member states, published after May triggered Article 50 to begin Brexit, have provoked consternation among British politicians.
Although it is part of the EU, Gibraltar is outside the Value-Added Tax area and the customs union - a group of states that have agreed to charge the same import duties as each other and usually allow free trade between themselves.
Gibraltar was captured by Britain in 1704 and ceded to Spain in 1713 under the treaty.
Number 10 played down Lord Howard's suggestion the United Kingdom might send a taskforce to The Rock-"it isn't going to happen", said a spokesman-but refused to condemn him.
Johnson said Gibraltar's sovereignty "is not going to change and can not conceivably change without the express support and consent of the people of Gibraltar and the United Kingdom". Picardo accused Spain of trying to "manipulate" Brexit negotiations in a bid to make a claim on the territory.
"Spain might like to use Gibraltar as a political pawn, the European Council may have allowed Spain to put this issue in this current draft of the guidelines, but Gibraltar is not going to be a political pawn of Brexit", he told British media Friday.