Home Office says in letter that it cannot give unilateral assurances until status of Britons in other EU countries is protected

The UK would lose “negotiating capital” in Europe if it unilaterally granted EU citizens the right to remain after Brexit, the government has said.

In a letter to a group of EU citizens from the office of the home secretary, Amber Rudd, the government said it “recognises that EU nationals make an invaluable contribution to our economy and society”.

However, in an apparent hardening of the official position, the letter warned that the government cannot do anything to address their position after Brexit until it has assurances that British citizens in Europe will receive reciprocal protection in the country where they have settled.

“Agreeing a unilateral position in advance of these negotiations would lose negotiating capital with respect to British citizens in EU member states and place the UK at an immediate disadvantage,” said the letter signed by Peter Grant, an official in the free movement policy team of the immigration and border policy directorate of the Home Office.

“The prime minister has been clear that she wants to protect the status of EU nationals already living here, and the only circumstances in which that would not be possible are if British citizens’ rights in other EU member states were not protected in return,” it added.

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Nicolas Hatton, the chairman of campaign group the3million, which represents EU citizens in the UK, said: “This is a very disappointing letter.Whatever happens in the negotiations, they will have to find a way to register 3 million people, and if they do not start this process early, it will be impossible.

“The Home Office is overwhelmed by [the backlog of 100,000] applications for permanent residency. The system is not working, but instead of addressing it, they just stick their heads in the sand. It is quite shocking really.

“It is quite clear that there is no change in their position and no recognition that the current system will not work.”

The letter has incensed members of the3million, a grassroots organisation founded by Hatton and a group of French citizens in Bristol following the EU referendum in June last year.

One member wrote on a closed Facebook group on Monday: “We have been referred to as ‘main cards in the negotiations’, ‘bargaining chips’ and now ‘negotiating capital’. Does that make you feel valued?”

Another said: “We are, it seems, not really people at all, just ‘negotiating material’. I have never been described as a ‘chip’ or ‘material’ before. Surely this is discriminatory language prohibited under equality laws?”

The letter was sent in reply to one from the3million before Christmas warning Rudd that up to 1 million EU citizens could face deportation after Brexit, unless the Home Office came up with a simple way of recognising their status in Britain.

The group is concerned that families with one or more EU citizens are becoming collateral damage in Brexit talks, facing stress and anxiety because their right to remain will not be enshrined in law when the UK leaves the EU.

Some EU citizens who have been in the UK for more than five years are seeking paperwork to support their status, a process that entails filling in an 85-page application form for permanent residency that was designed for non-EU citizens coming to Britain.

Hatton said others who have been in the UK for less than five years are opting for a “residency certificate” to enable them to provide proof that they were in the country before the referendum.

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Completing both forms involves a large number of supporting documents. They have been criticised as unfit for purpose.

The permanent residency form requires evidence of every absence out of the country and, in some cases, such as stay-at-home parents, proof of comprehensive sickness insurance.

This has come as a shock to many, including Britons married to EU citizens whose partners have stayed at home to bring up children. It may also cause problems for those who find that a five-year continuous period in Britain does not qualify them for residency, if they have taken a year or two out of work.

Hatton pointed out that the systems deployed by other EU member states for EU residents who are not nationals are much simpler.

“The amount of proof they require in this country is quite ridiculous and I wish that the Home Office would have at least started to think about that and think laterally,” he said.

Several EU citizens who have contacted the Guardian, including German neuroscientist Sam Schwarzkopf, received letters asking them to make preparations to leave the country, even though they have been in the UK for more than a decade.