Local authorities could have to issue up to 3.5m identity cards as part of the government’s plan for mandatory voter ID, it has emerged, prompting warnings over potential high costs and disruption for councils.

Ministers have yet to set out how the scheme, announced in the Queen’s speech, will work in practice, or when it will begin. But it has pledged that would-be voters who do not possess the necessary photo ID can apply to their council for a free “voter card”.

A government-commissioned report on access to ID has suggested that more than 2 million adults might lack the necessary documents to vote under the new system. An analysis by an elections expert has suggested that considerably more might seek the voter cards.

Northern Ireland introduced mandatory voter ID in 1985 after sectarian-based attempts to rig elections through multiple votes. When a photo requirement was introduced in 2003, as well as being allowed to use a wide range of existing documents, people could apply for an electoral identity card.

In the first two years of the scheme, about 97,000 cards were issued, with an average of more than 19,000 a year since. Extrapolated to the population of the rest of the UK, this could mean close to 3.5m voter cards being requested at the start of the scheme and almost 700,000 a year after that.

Stuart Wilks-Heeg, an expert on election processes at the University of Liverpool who carried out the analysis, said it would “represent a huge challenge”, particularly as the work would be carried out by under-resourced local election teams.

He said: “The government needs to be clear about how the issuing of such cards will be funded and how common standards of service will be guaranteed for electors across the country.”

The Cabinet Office, which is responsible for elections, notes that the Northern Ireland cards can be used for proof of age and other purposes, whereas the GB ones will not, which will mean demand for them will be lower. It says central government will cover the costs of the scheme, but has not yet said how.

Labour and Conservative council leaders have told the Guardian they have received no information yet on how the voter card scheme will work, or who would pay for it. One Labour leader said: “It’s another case of the government just doing things to us.”

Nick Forbes, the Labour leader of Newcastle city council, said: “I can’t see how they can justify trying to introduce them through the back door, without giving councils any resources or funding to do this, and simply expect councils to, yet again, pick up the pieces. The costs for councils will be considerable.”

The Local Government Association, which represents councils, and the Association of Electoral Administrators, the body for local election officials, have said ministers must ensure the voter ID system does not finally penalise councils, or put off certain groups from voting.

Critics say the new system addresses a problem that barely exists in the UK outside Northern Ireland, and risks disproportionately hitting older, disabled and homeless voters, who are less likely to have appropriate documents. US civil rights groups have warned that it amounts to Republican-style voter suppression.

Nonetheless, the measure appears unlikely to face much of a challenge passing the House of Commons, despite criticism from opposition parties, with the only Conservative MP to have so far come out publicly against it being David Davis, a longstanding campaigner on civil liberties issues.

Other libertarian Conservatives such as Steve Baker, who have, for example, opposed domestic Covid certificates, are supporters of voter ID across the UK.

Another Tory MP from that wing, Sir Charles Walker, said he did not oppose the plan, but wanted to make sure the system did not exclude people. “I think all advanced democracies should be confidently seeking to approve integrity of the electoral process,” he said. “I look forward to the legislation being published, and the debate will have to focus on how we ensure that in tightening processes people are not disfranchised, for example those without driving licences or passports.”