Britain’s decision to relinquish control of the Chagos Islands does not signal a change in the government’s position on other overseas territories, Foreign Secretary David Lammy has said.

He told the Commons the status of the Falkland Islands, Gibraltar and other British Overseas Territories are “not up for negotiation”.

It comes after the government announced it would give up sovereignty over a cluster of remote Indian Ocean islands, a move which follows years of diplomatic talks and international pressure on the UK to resolve their disputed status.

Meanwhile, Chagossians who oppose the deal to hand control of the islands to Mauritius have staged a protest outside Parliament.

Lammy described the deal with Mauritius – which has long argued that it was illegally forced to give the islands away in return for its own independence from the UK in 1968 – as a “historic moment” and a “victory for diplomacy”.

A key component of the deal announced last week, which is expected to be ratified in 2025, will allow the UK and US to continue to operate a strategically located military base on one of the islands, Diego Garcia.

While the UK’s move to renounce claims to the Chagos Islands has received praise internationally, including from the US, critics say it could embolden governments which claim sovereignty over other British Overseas Territories.

Lammy told the Commons the particular circumstances around the Chagos Islands are “not comparable” to other territorial disputes, in particular Gibraltar and the Falkland Islands – which the Spanish and Argentine governments respectively claim rights over.

“The government remains firmly committed to modern partnerships with our overseas territories based on mutual consent,” he added.

Tory shadow foreign secretary Andrew Mitchell criticised the agreement, saying it gives “succour to our enemies in a dangerous world, and undermines the strategic web of Britain’s defence interests”.

Soon after the deal was announced, the Argentine government restated its claim to the Falkland Islands. The British governor of the islands reassured its people about the deal and said the “UK’s unwavering commitment to defend UK sovereignty remains undiminished” in light of the Chagos Islands agreement.

While Britain has apologised for the forcible removal of around 1,000 Chagossian islanders in the 1960s, many of the island’s diaspora do not support Mauritius’s territorial claims.

Some Chagossians who live in the UK say they were not consulted on the recent agreement. A group gathered in Westminster while Lammy made his statement.

Ingrid from Crawley said: “It was like somebody stabbed you from behind. Our heart was broken because they just took the decision.

“We don’t have a say, it’s as if we don’t count. We are just like their puppets. Where are our human rights?”

Bertrice Pompe from Clapham Junction said Chagossians had been very poorly treated, adding “to them, we are not human”.

She continued: “I’d love to go back… I’d love to go there for longer than one week.

“The UK is not my country but I have to be here just to try get back to where I belong.”

Mylene Augustin from Crawley demanded the government “stop the suffering”, adding: “Let my people, let us decide for our future.

“This is our island, this is our heritage.”