Britain’s “hardening” attitude to asylum seekers threatens to end one of the last safe routes for children to reach the UK, Alf Dubs has said.

Lord Dubs believes the Home Office is targeting a permanent reduction in childrens’ rights, under an EU law known as the Dublin regulation, to join family in the UK after Brexit.

“I fear they want to get rid of family reunion,” said Dubs, who escaped the Nazis and was brought to Britain from Prague through the Kindertransport programme in 1939.

“There is a new home secretary, policy is hardening and [the loss of family reunion] is a pretty depressing aspect. These children are in terrible conditions in France and Greece.”

Dubs, who was behind the rescue of hundreds of children from Calais three years ago, presented a petition to save family reunion to the Home Office on Thursday.

The petition, which 80,000 people have signed, was started after the Guardian revealed last month that the “Dublin law” – which allows children stranded in Europe to join family in the UK to claim asylum – will end immediately if there is a no-deal Brexit. Even if Britain leaves with a deal, an alternative will need to be negotiated as part of transition agreements.

Under the EU (Withdrawal) Act 2018, the government is committed to discussing a replacement for the law, but politicians and campaigners say they have seen no evidence that proper negotiations are taking place. They fear the intention is to rely solely on national law, which only allows parents and children to reunite.

Dubs said: “If the government don’t negotiate, there will be no rights for children at all. The government say they will rely on national laws, these are very limited. Under [EU law] they can join uncles, aunts, siblings. It’s pretty hard if they can’t join a sibling. It’s not a big ask on our part.”

Yvette Cooper, who sits on the home affairs select committee, said: “It is deeply worrying that the current system for family reunion would stop completely in a no-deal scenario. And while the government has said it wants to replicate the current family reunion arrangements, it is not yet apparent how it intends to honour that commitment.

“Given the effect the onset of winter could have on many unaccompanied child refugees, we need these assurances immediately.”

The Home Office said action is being taken to look at how family reunion will be replaced in the longer term.

“Deal or no deal, cooperation will continue on asylum and returns,” said the statement. “We have taken the proactive step of writing to the European commission making clear we are seeking to negotiate a replacement mechanism for unaccompanied asylum-seeking children to join their family members in the UK, once we leave the Dublin regulation.”

Lord Dubs said he is also concerned that current child refugee commitments are being deliberately ignored.

“We are also bringing this petition because they are dragging their heels on bringing children here. They seem to have stopped taking them under my amendment, they are not even meeting their own capped target [of 480 children].”

The charity Safe Passage, which works closely with many families trying to bring children to the UK from camps in Greece and France, said there has been an increase in calls from families worried about how they will bring children over after Brexit.

Beth Gardiner Smith, CEO of Safe Passage, said: “When safe and legal routes aren’t available, dangerous journeys are often the only option people have to join family or reach a place of protection. Without action now from the government, hundreds of children could be stranded in Europe and take deadly risks to reach their family as a result.

“More safe and legal routes are the best way to break the business model of the traffickers and organised gangs who trade in human lives. The government must act now to keep family reunion open, whatever happens to Brexit.”