Calls for the government to speed up the evacuation of gay, lesbian and transgender Afghans intensified on Saturday after the first LGBTQ+ group arrived safely in Britain but left many behind to face an uncertain fate.

The group of 29 is “hoped to be the first of many” in the coming months, the Foreign Office said, hours after the Taliban announced LGBTQ+ rights would not be respected.

The move has left large numbers of LGBTQ+ individuals linked to the previous administration stranded in Afghanistan, with calls growing for the UK to broker a rapid mass evacuation from Kabul.

One of the 29, who did not wish to be named, told the BBC on Saturday that he felt “like a human being” for the first time in his life. “Everything collapsed after the fall of Kabul. I was very depressed. I was counting my days to die.”

He said Britain was now his home. “Everything is new to me here. A new lifestyle, a new language and culture. I am a bit nervous about my future, and I am trying to figure out where to start my new life, but man, I feel safe and free! This is amazing.”

Gianluca Di Caro, chief executive of the British and Irish Boxing Authority (Biba), said the organisation had 250 boxers and their families still trapped in Afghanistan, a significant proportion of them LGBTQ+.

Di Caro told the Observer: “We need to get them out quickly. We’ve already had female boxers who have been assaulted by the Taliban. In some cases Taliban have gone into some of the girls’ houses.”

Biba has been in contact with Home Office officials since the Taliban’s return to power on 15 August, but fears time is running out.

Previously, a Taliban judge said there were only two punishments for homosexuality – stoning or being crushed under a wall. During the Taliban’s last period in power there were reports of gay men being stoned to death in officially sanctioned executions.

The UK foreign secretary, Liz Truss, said in a statement on Saturday: “We played a key role getting these people out and will continue to do all we can to help at-risk Afghans leave the country.” She added Britain would defend “the right of all people to be themselves and love who they want”.

Among the group are activists who had stood up for LGBTQ+ rights in Afghanistan, Foreign Office officials said. The arrivals will stay in “bridging accommodation”, they added, although their legal status is unclear.

No details were given on how the group were able to leave Afghanistan, with officials stressing the need to safeguard the route. Yet the fact they were allowed to depart suggests a possible diplomatic agreement. Truss’s predecessor, Dominic Raab, previously stated the need to engage with the Taliban.

Officials said the foreign secretary, along with British LGBTQ+ group Stonewall and Canadian organisation Rainbow Railroad, had intervened to ensure the Afghan group gained safe passage to the UK.

Nancy Kelley, Stonewall’s chief executive, said her organisation had been campaigning to bring vulnerable Afghans to the UK for a few months. She vowed to continue to push for international support to help those still in the country.

“The situation is likely to remain extremely dangerous for some time,” Kelley said.

LGBTQ+ people have previously described hiding in small rooms and basements for weeks after the Taliban takeover. Others are being hidden by friends, who are helping to keep watch and bringing them food and supplies.

The UK has evacuated more than 8,000 Afghans who worked for the UK and their families, as well as many other highly vulnerable people, since the Taliban seized power.

The government said that the Afghan citizens’ resettlement scheme would remain open to provide protection for people at risk.