Foreign Secretary Philip Hammond told Argentine counterpart Susana Malcorra that the UK’s position over the remote archipelago has not changed.
Relations with Buenos Aires have appeared to thaw since Cristina Kirchner left office last December.
The former president repeatedly raised the dispute with escalating rhetoric, insisting Argentina would never renounce its claims over the islands that it calls Islas Malvinas.
Mr Hammond underlined the result of the 2013 referendum that saw Falklanders vote overwhelmingly to remain a British overseas territory during the talks with Ms Malcorra, who is in London to attend the anti-corruption summit.
During a “warm” discussion, the ministers also covered trade, anti-corruption and efforts to tackle the drugs trade.
Mr Hammond said: “I was pleased to meet foreign minister Malcorra and we had a warm, wide-ranging discussion. During their meeting at Davos earlier this year, the Prime Minister and President Macri set out an aspiration to embark on a new phase of relations between our two countries.
“Foreign Minister Malcorra and I discussed how to take this forward by developing a strong relationship based upon areas of mutual interest, such as increased trade links, combating drugs, crime and corruption, and closer co-operation on science and technology.”
The meeting was the first discussion in London between UK and Argentine foreign ministers since 2002.