The government has called on EU leaders to publish concrete plans to preserve the rights of British citizens living on the continent post-Brexit.

The home secretary, Sajid Javid, said he was concerned that other EU member states have not stated how they are going to support Britons in Europe when the government has advanced plans for a new status for the estimated 3.4 million EU citizens living in the UK.

His concern was welcomed by the leading campaign group, British in Europe. But it added it was the government’s fault that they had been left in limbo.

“As Mary Berry might have said: this display of concern from the British government is a bit late and a bit rich,” said Jane Golding, a British lawyer based in Germany who is chair of British in Europe.

Details of the new ID scheme for EU citizens post-Brexit were due to be unveiled on Thursday morning and Javid said it was “not good enough” that other EU countries were not doing the same.

“Publishing details of how we will administer our settled status scheme shows we are honouring the commitments made towards EU citizens living in the UK.

“But I am concerned that I have not seen any similar plans on how EU member states are going to support British nationals in their countries. This is not good enough and I hope both the European parliament and commission will exert more pressure for them to do this as soon as possible,” he said.

The European parliament’s chief Brexit coordinator, Guy Verhofstadt, said he had ‘serious concerns’ over all citizens impactedaffected by Brexit. Photograph: Andy Rain/EPA

British in Europe said it did not want a mirror status to be introduced across Europe.

“What the home secretary appears not to realise is that it is the UK government that has thrown its own nationals in Europe into this uncertainty by insisting on introducing settled status for EU citizens in the UK so that it became an option for us in the EU27 in December’s last-minute deal. The EU27 was not interested in settled status up until then,” Golding said, who added that “Javid seems to be asking all the wrong questions.”

Golding said Javid should be seeking details from the EU27 on what it was planning to do “to tweak existing systems”. She also called on the home secretary, the prime minister, Theresa May, and the Brexit secretary, David Davis, to “come and talk to us about what people on the ground actually need rather than simply deciding what’s best for them.”

British in Europe complained last week that it represented “the forgotten victims” of Brexit with neither Brussels nor London taking up their fight to retain their rights.

Britons who live in Europe want to maintain free movement rights to allow them to continue to work freely and offer services across the continent; the “right of return” to the UK with their families without any immigration barriers for EU national spouses; and a guarantee that British children living in Europe can attend university as home students.

The Home Office is planning to publish a “statement of intent” on Thursday, which will be the first sight of the registration system that the former home secretary Amber Rudd had previously said would be “as easy as setting up an online account at LK Bennett”.

The European parliament’s Brexit coordinator, Guy Verhofstadt, said he had “serious concerns” over all citizens affected by Brexit and vowed to fight on their behalf.

“The European parliament will defend the rights of all those affected by Brexit.”

On Britain’s plans for a new immigration status for EU citizens, he said parliament “still has a number of very serious concerns”, including the need to better cater for vulnerable groups and the high application cost of £72. He said the process should be free.

He asked: “Why should EU citizens be financially punished for the Brexit referendum outcome?”