Thousands of lone parents living with young children in west London have been told they must go out and look for work.

At least 3,000 single mothers and fathers in Hammersmith and Fulham are known to be affected by changes to the benefits system brought in at the end of October, along with 2,750 people in Westminster and 1,670 in Kensington and Chelsea.

Parents of children over seven no longer qualify for Income Support and instead receive Jobseeker's Allowance, which requires claimants to actively seek work and which previously applied only to those with children older than 10.

The move is part of a wide-ranging reform of the welfare state by the coalition government, which is also seeking to introduce a cap on housing benefit that could affect tens of thousands more residents in the three boroughs.

Announcing the changes, work and pensions minister Maria Miller said: "We know that work is the best route out of poverty. This is why lone parents with younger children will now be able to have access to help and support to look for work through Jobcentre Plus.

"Getting a good balance between work and family responsibilities is important for every parent. Job Centre Plus advisors will actively support lone parents so that they can get that balance right too."

The new rules mean parents of children under 12 will be able to specify jobs which fall within school hours, and childcare responsibilities must be taken into account when judging a parent's availability to work.

But the move has drawn fierce criticism from local Labour councillors, who say lone parents already struggling with childcare will be hit hard by the measures.

Stephen Cowan, opposition leader in Hammersmith and Fulham, said: "Some of the cases that I'm already aware of as a result of this policy are heartbreaking. How the Conservatives can claim with a straight face that they are progressive or compassionate is beyond me, when there is clear evidence that they are cruel and oblivious to the pain they are causing.

"What this will mean is that even if you are a lone parent looking after a child with a disability that requires day and night attention, you will be told that you have to go out to work."

According to the Department for Work and Pensions, all parents now looking for employment will be offered training opportunities, job application advice and financial grants to help them return to work.