Plans to end freedom of movement for EU citizens immediately after a no-deal Brexit have caused anxiety and confusion among European nationals in the UK, with concerns they could be caught up in hostile environment policies.

Downing Street confirmed rules allowing EU nationals to live and work freely in the UK would end abruptly if the UK leaves the bloc without an agreement at the end of October.

In theory, the rights of EU citizens who have permanent residence in the UK should not be affected and they will continue to be allowed to apply for settled status – granted once they have lived in the UK for five years – until the end of December 2020.

However, news of a possible sharp end to free movement without the transition period envisaged under Theresa May’s administration provoked concern about how at least 2.6 million EU nationals who have yet to apply for settled status would prove they are in the UK legally.

The3million, which represents EU nationals in the UK, said plans by the home secretary, Priti Patel, to impose new border restrictions overnight on 31 October if Britain leaves the EU without a deal were “reckless”.

Nicolas Hatton, a co-founder of the group, said: “Ending freedom of movement without putting legal provisions in place for those EU citizens who have not yet successfully applied through the settlement scheme will mean that millions of lawful citizens will have their legal status removed overnight.”

Concerns were heightened with the leak of an internal government discussion paper warning introducing a sharp cutoff date could present “legitimate concerns of another Windrush”.

Since March, 1 million EU nationals have successfully applied for settled status, giving them the right to live in the UK after Brexit.

Some of those who have yet to apply are worried about their right to NHS treatment or employment being questioned. Some are also concerned about how they would prove they have the right to live in the UK if they travel abroad.

Stephanie Dawoud, a spokeswoman for Imix, an immigration communications charity, said: “The fear is that the hostile environment will be applied to EU citizens who are living here legitimately. There is no system in place to distinguish between the people who have been living in the UK before Brexit and someone who has arrived on 1 November.

“It will be up to employers, the NHS and landlords to check whether someone has the right to be here or not. It is another announcement that feeds into the worst fears of EU citizens in the UK.”

Some EU nationals have not applied for settled status because the digital application process is yet to be available on iPhones, although this should be resolved before the end of the year. Campaign groups say large numbers of people who are required to apply for settled status are still unaware they need to do so.

There was dismay about the absence of clear information about what kind of documents people might need to take with them if they were to travel abroad, returning after 31 October.

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Gregorio Benincasa, an Italian citizen living in the UK who has yet to apply for settled status, said: “Are we expected to carry reams of documentation proving that we’ve built a life in the UK over the last decade? Will border guards be responsible for reviewing our employment contracts and utility bills to prove our status?”

Christian Wuff, a finance project analyst who has been in the UK since arriving as a student from Norway, said: “This is very scary stuff. What if I need a new bank account, a new mortgage, a new job? I’ve been here 19 years without ever having to show anything other than my passport. Now I’m having to apply to stay in my own home.”

The Home Office urged EU nationals to apply for settled status to avoid potential difficulties. Officials said no one eligible for the status would be barred from re-entering the UK if and when free movement ended, but it was not clear how checks would be made.

Under May’s government, there was an acceptance the new immigration system and border controls would not be ready for an immediate change, so a transition phase was envisaged until they were put in place. This now appears to have been dropped.

The Conservative MP Alberto Costa, a campaigner for EU citizens’ rights, said: “The government are creating deep confusion as to what will happen. No details have been given on how the government would distinguish between the rights of EU nationals lawfully in the UK pre-Brexit from those who come into the country after 31 October.”

He said he was concerned about the lack of detail from the Home Office. “Is there going to be a total block on all EU nationals coming into the country post-Brexit? Or will all lawfully resident EU nationals be expected to show some form of settled status evidence? What about the 2.6 million people who have not yet registered?” Costa asked.

“If we don’t do this correctly, it’s not just about lorry queues on the road to Dover, it’s about denying people their basic rights – rights to reside, rights to healthcare, rights to pensions.”

Costa also warned of a reciprocal sharp end to free movement for the 1.3 million British citizens living in other EU nations. “Their rights would also end abruptly. It is unclear how the British government would protect their rights,” he said.

A Home Office spokesperson said further details were being worked on and would be announced shortly. “EU citizens and their families still have until at least December 2020 to apply to the EU settlement scheme and 1 million people have already been granted status,” they said.

“Freedom of movement as it currently stands will end on 31 October when the UK leaves the EU, and after Brexit the government will introduce a new, fairer immigration system that prioritises skills and what people can contribute to the UK, rather than where they come from.”

In a sign of further confusion over the government’s policy, a senior Whitehall source said the only change that had so far been confirmed by the Home Office was additional criminal record checks on those entering the UK, while other potential changes were still being assessed.

“I don’t think anyone is leaning in to the fact that there will be a spanking new system in place,” the source said. “The change is a symbolic gesture towards the many voters who supported Brexit because they wished to stop the free flow of people into the UK.

“The home secretary and the PM think that ending freedom of movement is an integral part of taking back control. The reality is that time is so short that … it may not look a whole lot different from the policy the previous government set out.”