The government’s proposed benefit cap will apply to carers looking after their disabled offspring, forcing some parents to move out of their home or put their child into care, it has been confirmed.

Ministers have repeatedly said disabled people will be exempt from the £500-a-week benefit cap that is due to come into force in April.

But they have now accepted that if a parent is still looking after a disabled child after they reach adulthood, even if the child’s mental age is as low as eight, the parent and the child will be treated separately, and the parent will be subject to the benefits cap.

In the Commons last week the work and pensions minister Esther McVey said: “In practice most carers will be exempt [from the cap] because their partner or child is in receipt of disability living allowance.”

She was then pressed by the Labour MP Andrew Gwynne to look at the rules again. He said: “Close reading of the regulations indicates that a household comprising parents and a disabled adult dependant receiving disability living allowance will not be exempt from the cap, despite the minister’s promises that they would be.”

McVey then admitted: “Should there be another adult in the house, that is then a separate household, so both have to be assessed separately.”

The change in the rules is already starting to bite with letters being sent to carers with offspring aged over 20.

Jacqueline Smirl from Maida Vale in north-west London has been told she is to lose roughly £80 a week even though she looks after her 20-year-old son, who is in need of 24-hour care and has the mental age of an eight-year-old owing to autism.

She told the Guardian: “The ridiculous thing is that the cap came in to incentivise people to go to work, but I cannot go to work because I am looking after my son full-time, and I am, in the process, saving the government money.”

She said she had received a letter last week from the Department for Work and Pensions telling her she was subject to the cap. She claimed many other parents, especially in the south-east, would be in the same position.

After the admission in the Commons last week McVey was pressed again by Karen Buck, the MP for Westminster North, the constituency in which Smirl lives.

Buck said: “Ministers have repeatedly stressed that a household containing anyone in receipt of disability living allowance will not be affected by the benefit cap, but constituents of mine who have an adult disabled child are now being told they will be affected by the cap because the regulations appear to state that if a family has an adult severely disabled person living in the household, that person is not a member of the household.”

She asked: “Please will the minister clarify whether the benefit cap will apply to someone who is looking after a severely disabled adult child?”

McVey replied: “A household is a basic family unit, and for the purposes of paying out-of-work benefits that will be a single adult or a couple and children, so once another adult is in the house, that is a separate household.”

She said discretionary payments were available to prevent hardship, but these are temporary.

Smirl has lived in Maida Vale since 1984. She lives in a £400-a-week private rented property and says her son is willing to move to a council property but none are available, forcing her either to leave the area or to put her son into care.

She said the threat of disruption to her already difficult life was putting intense pressure on her and she was receiving counselling.

Smirl has also written to the work and pensions secretary, Iain Duncan Smith, to examine the anomaly. She writes: “If I’m displaced, my son is displaced. My son is likely to be dependent on myself for the rest of his life and I have accepted the full-time job of looking after him. I do not want to give him up to the state at an enormous increase to the public purse.”

She points out that if she were looking after a partner, spouse or “child” she would be exempt from the cap.

“The benefit cap is to motivate people into work. I already work more than full time. I do it all by myself, with very little support and now I am put in this terrible situation,” she writes.

Buck said: “Ministers have frequently stated that a household where someone is severely disabled and in receipt of disability living allowance will not be affected by the benefit cap. It is now absolutely clear that assurance is absolutely worthless.”

She added she would be tabling questions to ascertain the precise number affected, and predicted it would run into the thousands.