Thousands of families will be paid up to £4,500 to compensate them for benefits lost when a teenager takes up an apprenticeship.

Critics say the plan, unveiled by the Prime Minister on Tuesday, underlines the madness of the welfare system – and raises questions about his commitment to cutting the bloated benefits bill.

Government sources insisted Andy Burnham‘s plan would only apply to a ‘small’ group of disabled youngsters whose single-parent families would otherwise be more than £80 a week worse off because of a quirk in the welfare system.

But former Tory work and pensions secretary Sir Iain Duncan Smith said: ‘We should not have a system where people are better off sitting at home than they are doing a job, and that includes apprenticeships.’

He added: ‘If there is a problem with apprenticeships struggling to compete with the benefits system then the benefits should be cut.

‘Paying bursaries on top is piling payments on payments – it just complicates a system that is already a mess.’

The scheme is aimed at teenagers, numbering in the ‘low thousands’, whose families would be left worse off if they did an apprenticeship.

Around £30million has been earmarked to fund the annual payment. It applies to 16 and 17-year-olds registered as having a disability and living in a single-parent household.

Andy Burnham, pictured with Education Secretary Lucy Powell, visited Alstom Transport in Derby on Tuesday as he pledged action to tackle Britain’s youth unemployment crisis

Work and Pensions Secretary Pat McFadden insisted the welfare system should be a ‘springboard to opportunity, not a barrier to it’ as he set out Labour’s plans

If they remain out of work, the family qualifies for up to £340 a week in extra benefits, which is lost if they take up an apprenticeship where pay is typically £258 per week.

Ministers fear some parents are dissuading youngsters from taking an apprenticeship because it would leave them £82 a week worse off.

Mr Burnham has signalled that he wants to rein in the benefits system but has yet to publish any concrete proposals for short-term savings.

Speaking at the weekend, he ruled out ‘crude cuts’ but suggested that some payments could be made ‘conditional’ on people taking up work-related opportunities.

Left-wing Labour MPs, who blocked Sir Keir Starmer’s bid to trim the welfare bill, said on Tuesday they will not tolerate any cuts.

Apsana Begum, MP for Poplar and Limehouse, said Labour ‘were elected to deliver change, not cuts’, adding: ‘I will stand with disabled people, against any further cuts and restrictions to their benefits.’

Liverpool Riverside representative Kim Johnson said: ‘If the new leadership believes it can revive the failed politics of welfare cuts instead of asking the wealthiest to pay their fair share, it will be repeating not only Keir Starmer’s mistakes but 14 years of Tory austerity.’

She told Bloomberg: ‘If the first instinct of a new leadership is to target disabled people and low-income families… then nothing has been learnt.’

Analysis by the Daily Mail reveals that Mr Burnham has handed government roles to 18 MPs who joined the rebellion against welfare cuts last year

They include his deputy Louise Haigh and Chief Whip Anneliese Midgley, who were two of the leading figures in the revolt. Housing Secretary Angela Rayner was also a key figure in forcing Sir Keir to back down.

The Conservatives’ work and pensions spokesman, Helen Whately, said: ‘This is a reminder that Labour MPs don’t back welfare savings. In fact, they just want to tax people more – to spend more on benefits.’

The new bursary scheme is part of a wider package aimed at tackling the growing ‘Neets’ crisis.

The number of young people not in education, employment or training has now topped one million and represents 13.5 per cent of all 16-24 year olds.

Work and Pensions Secretary Pat McFadden acknowledged that the welfare system is acting as a ‘barrier’ to work for some, but said the bursary scheme would help youngsters unlock their potential.

He added: ‘By providing bursaries to those who need them most and fully funding apprenticeship training, we are making sure cost is not the reason someone misses out.’

Meanwhile, Mr Burnham called for schools to adapt their curriculum to meet the needs of local employers and help stem the youth jobs crisis. The PM said youngsters should be given the chance to focus on technical education from the age of 14.

Business leaders welcomed the move but said Labour must do more to ease the cost of hiring young people after hikes in national insurance and the minimum wage.