Brexit Secretary Stephen Barclay has asked the EU to consider a separate agreement on citizens’ rights in the event of no deal.
Around 1.3m UK citizens live in one of the other 27 EU member states, while the UK hosts about 3.2m EU nationals.
Theresa May’s Brexit deal covers citizens’ rights but the deal has not yet been approved by MPs.
The EU said the best way to safeguard citizens’ rights would be to agree the withdrawal agreement.
The Tory MP, Alberto Costa, who has campaigned on the issue, told the BBC: “Better late than never.
“The UK government has finally taken seriously the Costa amendment and with the spectre of no deal appearing ever closer, the UK government are worrying about how to protect the rights of British citizens in the EU in the event of no deal.”
Mr Costa said it was important to reach a separate deal on citizens’ rights “given that we will shortly have a new prime minister with very little time to negotiate anything of substance with the EU ahead of the 31 October deadline”.
“Failure, will result in a total loss of rights for British nationals in the EU, confusion over pensions and welfare access, and undoubtedly a tsunami of litigation against the failure of the UK govt to protect their rights.”
Mr Costa is calling on all of the leadership candidates to commit to changing the law as soon as possible should they win.
Only Michael Gove so far as promised to do so and has received the backing of Mr Costa as a result.