The government is refusing to pay the £65 fee for EU nationals employed in the civil service to register their right to remain in the UK.

In a parliamentary answer this week to a question asking if the government would cover the fee for civil service workers, the Cabinet Office minister Oliver Dowden said they would have to pay for themselves – and admitted that the government had no firm idea how many EU citizens it employed.

Some employers have decided to pay the fee – including the Scottish government and London’s Islington council in the public sector – but ministers have declined to do so, arguing that it is “set at an affordable rate”.

The decision has prompted a complaint from the civil service union Prospect, whose deputy general secretary, Garry Graham, said: “It is unbelievable that the same government that has just spent over £50,000 creating a fake traffic jam in Kent continues to believe that paying £65 to permanently secure the future of their own staff is not a good use of money.”

Responding to a question from the Labour backbencher Alison McGovern, Dowden said: “The number of non-UK EU citizens employed across the civil service is not consistently collected across government, therefore it is not possible to estimate the cost of not charging for settled status for non-UK EU nationals employed directly by the government.”

There are 430,000 civil servants in the UK, according to the ONS, but a year ago it emerged that 15 out of 19 government departments do not know how many EU-born officials they employ – even though the proportion could be as high as one in 25.

One of the few that did, the Department for Business, Energy & Industrial Strategy, said just over half its 4,200 staff had voluntarily declared their nationality and of these 4.5% were EU nationals. But it is unclear if these figures would be replicated more broadly.

On Wednesday, Islington said it was the first council in the country to pay the Home Office fees for directly employed council staff who were EU citizens. It estimates there are 1,250 EU citizens and others who would need to apply to secure settled status to remain in the UK, at a cost of £80,000.

The government has demanded that the 3 million EU nationals legally resident in the UK complete paperwork to prove their right to remain and access public services permanently after Brexit – and insisted that applicants pay £65 to complete the paperwork.

McGovern said the government should reverse its policy and pay the fee for its employees, adding: “The fact that the government has no idea how many European citizens it employs tells you all you need to know about the shambolic Brexit preparations.”