British sovereignty of the Falkland Islands and Gibraltar is not up for negotiation, Sir Keir Starmer has said, as he told MPs the islands “are British and will remain British”.

Concerns over the territories were raised after the Government announced its decision to relinquish sovereignty over the Chagos Islands, and Argentina vowed to gain “full sovereignty” of the Falkland Islands.

Foreign Secretary David Lammy faced angry scenes and heckling in the Commons on Tuesday, as he delivered his statement on the deal with Mauritius.

The UK Government wants the treaty signed and ratified in 2025, Mr Lammy said, arguing it is a “historic moment” which has “saved” the joint UK-US military base on Diego Garcia, the largest of the islands.

During Prime Minister’s Questions, Sir Keir said: “My uncle nearly lost his life when his ship was torpedoed defending the Falklands, they are British, and they will remain British. And sovereignty in Gibraltar is equally not to be negotiated.

“Of course we will do everything we can to make it easier for all businesses to trade more freely so that we can grow our economy. I’ve been very clear about the Falklands, it’s personal to me.”

Sir Keir has previously spoken about his uncle Roger who served in the Falklands on HMS Antelope. In a speech in June this year, he said: “I remember the terrible wait when his ship was bombed. My mum’s fear as she sat by the radio every day, listening for news, and then the relief, a long week later, when we found out he had survived.”

The Prime Minister’s comments on Wednesday came in response to Liberal Democrat leader Sir Ed Davey, who said: “He’s right to say one of the many problems for our economy coming from the dreadful Brexit deal was the red tape that is being put on businesses.

“Now there are many examples of that, but a new example came to me earlier this week and it affects fisherman in the Falklands, who are otherwise having to pay huge amounts in tariffs to be able to sell their produce into the European market, or sail under a Spanish flag.

“So when the Prime Minister renegotiates the trade deal, can he remember the overseas territories and ensure that British citizens fishing off the Falklands can sail proudly under the Union Jack?”

Last week, Argentina’s foreign minister, Diana Mondino, promised “concrete action” to ensure that the Falklands, the British-controlled archipelago that Argentina calls the Malvinas and claims as its own, are handed to Buenos Aires.

“Following the path we have already taken, with concrete actions and not empty rhetoric, we will recover full sovereignty over our Malvinas Islands,” she said.