Worried citizens’ groups have dismissed Theresa May’s claim that a deal to guarantee their rights after Brexit is within “touching distance”.

A parliamentary inquiry was told the statement was hugely optimistic given that the Brussels negotiations are still in a state of “deadlock”.

The Prime Minister has tried to calm mounting anxiety by insisting the UK and EU can reach a deal on citizens’ future rights “in the coming weeks.”

But Jane Golding, the chairwoman of the British in Europe group, representing ex-pats, said: “We don’t see a solution as being within touching distance.”

While progress was being made on health and social security issues for the retired, the picture was much gloomier for younger people, she warned.

The two sides were still far apart on reunion rights with family members and, for example, the right to run a business in future, she warned.

“We think that much less progress has been made with regard to working citizens - and that’s on both sides,” Ms Golding told the inquiry by the Lords EU Justice sub-committee.

The gloomy message was echoed by Professor Stijn Smismans, of Cardiff University, who is advising the 3.4m EU citizens living in the UK.

“There is a kind of deadlock at this moment, because the premises of both sides are different,” he said.

The UK planned a new “settled status” for EU nationals in this country, but the EU was concerned that it would be based on UK immigration law, removing some rights.

There was also uncertainty about how it will be introduced and guaranteed in future – after the Prime Minister ruled out oversight by the European Court of Justice.

Professor Smismans said the Home Office had failed to issue “clear proposals” about a new registration procedure, which the European Parliament has warned could be illegal.

“As long as we don’t know that procedure, it could be 1m out of 3m excluded in practice – we don’t know. People are very anxious about it,” the politics professor told the peers.

The warnings come after Ms May sought to win over EU citizens in this country by promising them a closer involvement in a “streamlined” process to obtain “settled status” to stay after Brexit.

In an open letter, sent directly to 100,000 citizens who have asked to receive updates, the Prime Minister claimed an agreement with the EU was within "touching distance".

And she announced a new “user group” would be set up with officials, to give EU nationals a direct say over how the process works, to ease their "anxiety".

However, the Prime Minister is still refusing a unilateral guarantee of future rights should the withdrawal talks collapse and Britain leaves with “no deal”.