Millennials and gig economy workers face a pension squeeze in retirement despite the latest government efforts to prepare the public for their old age, with more than a third of the workforce still under-saving.

The Department for Work and Pensions published an analysis on Sunday saying 900,000 extra people would be drawn into workplace pensions after 18 to 21-year-olds were automatically enrolled by their employers from the mid-2020s. The DWP also said it would scrap an arrangement that sees pension contributions only based on earnings above £5,876, boosting retirement savings by £2.6bn.

But the government admitted there were still about 12m individuals under-saving for their retirement, representing 38 per cent of the working age population.

Despite the growing number of people working in the gig economy, and a promise in the Conservative party’s pre-election manifesto, the government did not extend “auto-enrolment” to the self-employed, instead saying it would explore using technology to encourage them to save.

Steve Webb, a former pensions minister now at the insurer Royal London, said that while extending auto-enrolment to 18-year-olds was a good idea, the proposed pace of change — to implement the reforms in about seven years — was “shockingly lethargic”.

“Those who never got to join a final salary pension and who have only recently come into pensions through automatic enrolment need urgent action to help them build up a decent pension pot,” he added.

David Gauke, secretary of state for work and pensions, said there had been “much greater savings into pensions” since auto-enrolment was introduced in 2012 and that extending the practice to 18-year-olds would “get more people into the habit of saving”.

He added in a BBC interview that opt-out rates from auto-enrolment had been “lower than people expected — and in particular lower for younger people”.

It was widely expected that the government would move to bring 4.8m self-employed individuals into auto-enrolment but the DWP said it would instead test a series of “targeted interventions” to increase self-employed pension contributions.

The number of self-employed people saving into a pension is falling sharply — from 1.1m to just 380,000 between 2001 and 2015 according to the Pensions and Lifetime Savings Association.

Workers with several jobs, and lower earners on salaries below £10,000 are also being left out of the pensions reforms. The DWP said workers would still need to earn over that threshold in one workplace to qualify for auto-enrolment, leaving those working part-time or with multiple jobs at a disadvantage.

According to the DWP, 13 per cent of workers with more than one job do not qualify for auto-enrolment, despite earning more than £10,000 in total. In total some 8m people have not benefited from automatic enrolment because they do not meet age and earnings criteria.

“The review has missed a vital opportunity to bring more low-paid workers into workplace pensions, leaving millions of women out in the cold,” said Frances O’Grady, general secretary of the Trades Union Congress, the umbrella body for trade unions representing 5m workers. “If the government doesn’t fix this problem, pensioner poverty will increase.”

This year a YouGov survey found that 51 per cent of 398 small and medium-sized businesses were in favour of bringing those earning less than £10,000 into pensions.

The UK ranks above the US, Canada, Australia and Germany in the share of self-employed people as a proportion of the total workforce and the swelling ranks of the gig economy mean more workers are classed as self-employed, without access to automatic pension provision.

380,000:            Number of self-employed people saving into a pension in 2015, down from 1.1m in 2001

Gig economy workers labelled as self-employed could be missing out on more than £22,000 in employer pension contributions, according to research by the Pensions Policy Institute for Zurich.

The organisation said this month that a typical gig economy worker earning £25,000 could end up with a final pension pot of £77,600 if auto-enrolled into a workplace pension.

Commentators said the difficulty of working out how to levy contributions from the self-employed was proving a stumbling block.

Tom McPhail, head of retirement policy at Hargreaves Lansdown, said: “The Treasury is not enthusiastic about using the tax or NI [National Insurance] systems to levy payments. However, there is no other ready-made mechanism to deliver the same kind of nudge solution which is working so well for employees.”

Auto-enrolment, introduced in 2012 as a way of halting the decline in workplace pension saving, has contributed to a record amount being saved. Workplace pension participation has increased from a low of 55 per cent in 2012 to 78 per cent in 2016, according to the DWP. In 2016, the total amount saved into annual workplace pensions by those eligible hit a record high of £87.1bn — the highest figure recorded in 10 years.

Kate Beioley and Josephine Cumbo in London