Up to 70,000 care home staff in England could leave the workforce or lose their jobs because the government is insisting they must be vaccinated against Covid, with women and ethnic minorities disproportionately affected, according to an official estimate.

In an impact statement from the government, officials believe between 3% and 12% of care home staff may still resist getting a Covid jab by the end of a 16-week grace period. The central estimate was that 40,000 could be left without jobs, but it could be as high as 70,000 or as low as 17,000.

In a separate statement on the public sector equality duty, the government said the policy of mandatory vaccination for care home staff was “likely to have a significant impact on ethnic minorities” as one in five members of the social care workforce are black, Asian or from another ethnic minority, a higher proportion than in the overall population of England.

It added: “The evidence suggests that vaccine hesitancy is highest among black people, people of Pakistani and Bangladeshi heritage, and non-UK/Irish white ethnic groups.”

The statement also acknowledged there was a “risk that issues such as lack of trust could be exacerbated by this policy” in relation to social care workers from minority ethnic backgrounds.

A group of Conservative MPs opposed to the policy had been repeatedly pressing the government to release an impact assessment before it called a vote on the issue last week.

Boris Johnson managed to get the policy through the House of Commons but there was a sizeable rebellion of more than 30 MPs who joined with Labour and other opposition parties in opposing the policy.

Defending the move in the House of Lords, James Bethell, a health minister, said: “We did not take lightly the decision to introduce this legislation. However, the risks that this winter will undoubtedly pose to the most vulnerable in our society make clear the choice that we must make, to do everything in our power to protect them.”

In response, Andrew Lansley, the Tory peer and former health secretary, said: “It is a step we should take only in a health emergency.”

The statement put the cost of replacing staff not meeting the vaccination requirement at £2,500 each, which based on government estimates “indicates a one-off cost to care home providers of £100m”.

It said: “This may place a temporary increased strain on those workers already vaccinated, until replacement workers are recruited.

“There is also an unquantified risk that some care homes who have higher levels of vaccine hesitancy amongst staff will find it more difficult or costly to replace workers.”