Stopping freedom of movement immediately on 31 October could lead to a situation like “Windrush on steroids” and the idea is “utterly ludicrous”, Jeremy Corbyn has said.

On a visit to Stevenage to see businesses engaged in no-deal preparation, Corbyn said: “Does that mean that a European Union national living in this country – possibly as a doctor, a nurse, a trauma surgeon, all kinds of things – goes home to see their family in Germany or Czech Republic or wherever else, they are not allowed back into this country? Is this another Windrush, on steroids?”

The government intends for EU nationals who arrive after 31 October to lose any rights under free movement law if the UK leave the EU without a deal.

The Windrush scandal, which led to the resignation of Amber Rudd as home secretary, exposed how the government was wrongly deporting people who could not prove their immigration status, having come to the UK from the Caribbean as children in the 1950s and 60s.

Two million EU citizens resident in Britain have not yet registered for settled status. The deadline is June 2021, or December 2020 if the UK leaves the EU without a deal.

Corbyn said he did not believe Boris Johnson was serious about any form of negotiation with the EU before the Brexit deadline in October. He said businesses he had spoken to were “appalled at the idea of a no-deal Brexit, and I think the prime minister should go and talk to them.”

He added: “He needs to recognise that just holding the threat of a no-deal Brexit on 31 October towards the European Union isn’t going to bring about a change, it’s going to make things much worse. He created this arbitrary date by his behaviour during the Tory leadership campaign. He needs to wise up and stop the nonsense with 31 October and start talking seriously.”

A Home Office source disputed the comparison to Windrush as they said EU citizens would have until December 2020 to apply for settled status. They said EU citizens would still be able to move freely between the UK and Europe until a new immigration system was put in place, apart from facing some extra checks to stop some categories of criminals entering Britain.

“Anyone comparing ending freedom of movement with Windrush is either not in possession of the facts or deliberately stoking fear,” the source said. “We encourage all EU citizens living here to apply for settled status through our scheme, which has already accepted over 1 million applications. In a no-deal scenario, the deadline of December 2020 is unchanged and it’s wrong and irresponsible to suggest otherwise.”

Diane Abbott, the shadow home secretary, said earlier that the chaos and confusion for EU citizens would make the Windrush scandal look like a “minor blip”.

Abbott told BBC Radio 4’s Today programme that EU citizens who had not registered would be “in the exact same situation as the Windrush people”.

“There are currently 3 million here altogether. A million have registered for settled status. There’s no possibility of two million registering between now and the 31st October, and then those EU nationals that were here but haven’t registered for settled status will be in the exact same position as the Windrush people,” she said.

“There will be people that came here perfectly legally but will not have the paperwork to prove that and will have all sorts of problems with employers and the NHS and so on.”

She said the abrupt policy shift was “typical of everything that Boris [Johnson] is doing on Brexit”.

The3million, which represents EU nationals in the UK, said the plans 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.”

There is particular concern about the absence of clear information about what kind of documents people might need to take with them if they were to travel abroad and return after 31 October.

A leaked internal government discussion paper warned that introducing a sharp cutoff date could present “legitimate concerns of another Windrush”.

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.