More than 13 million workers across Britain could be heading for a shortfall in the amount of pension they need for an adequate income, according to analysis.

The Pensions and Lifetime Savings Association (PLSA), which released the findings, said minimum contribution rates into workplace pensions should be increased to "at least" 12% to help remedy this.

It said automatic enrolment into workplace pensions, which started in 2012, is working well and will deliver a real improvement to the retirement incomes of millions of workers.

But it said currently, many people are not on target to reach an adequate retirement income as defined by the Pensions Commission over a decade ago - around two-thirds (67%) of pre-retirement income for a median average earner. For someone earning a median income of £27,456 this 67% figure equates to achieving a retirement income of £18,395.

According to the PLSA's modelling, as savings levels stand, of the 25.5 million people in employment across Britain - more than half - 13.6 million people - are at risk of not achieving this percentage pension replacement rate.

The report also estimates that 1.6 million people aged between 22 and 64 years old are at risk of falling short of a minimum income standard as defined by the Joseph Rowntree Foundation of £9,500.

It said millennials - those aged between 22 and 34 years old - face new challenges in saving, in particular, with the high cost of housing and accommodation, and many will have additional costs, such as student debt.

Meanwhile, many in generation X, aged between 35 and 54 years old, are currently making pension contributions which are too low to make up for their lack of saving earlier in their lives.

Baby boomers, those aged between 55 and 64 years old, faced a mixed situation, the report said, with some having built up very good retirement incomes from final salary pensions, and others having quite poor retirement income prospects. Even though some may now have been automatically enrolled into a workplace pension, many in this group will only have 10 years or less left of their working lives to turn their situation around.

Contributions into workplace pensions are made up of money from employees and employers as well as tax relief.

Minimum contributions are gradually being phased upwards, to reach 8% by 2019.

Savers may also need to consider working for longer, and using any wealth they have in properties, to achieve adequate incomes, the report said.

Graham Vidler, director of external affairs at the PLSA, said: "For younger savers increasing their automatic enrolment contributions from 8% to 12% and working slightly longer puts them on track for their target replacement rate.

"For older workers, who have less time to save, achieving their target replacement rate may also require a choice to save more and using other assets, such as property, if they have them.

"It is clear from our analysis that minimum contributions under automatic enrolment need to increase to at least 12%."

Mr Vidler said the precise level, the timing of the change and the balance between employer and employee contributions are issues which need further consideration.

He said a review, set to take place in 2017, "is an opportunity to start working towards this next phase of automatic enrolment".

Steve Webb, a former pensions minister who is now director of policy at Royal London, said: "This research shows the urgency of getting saving levels up."

He continued: "The best way to get people saving more is to make it the norm that when you get a pay rise you increase the contribution rate into your pension. Without urgent action, whole generations will simply be unable to afford to retire."