None of the main political parties has yet set out convincing plans on how they will improve the NHS, a leading health think tank says.

The Health Foundation said on current spending projections there appeared to be a £38bn-a-year shortfall in England in what would be needed by the end of the next Parliament.

The think tank said that would put plans such as tackling the NHS backlog, improving GP care and redeveloping hospitals at risk.

Neither Labour nor the Conservatives have said how much they will invest in the NHS, while the Liberal Democrats' pledge is well short of what the Health Foundation says is needed.

These were the only three parties the think tank looked at for its analysis.

Anita Charlesworth, a health economist from the Health Foundation, who used to be the Treasury’s director of public spending, said: “The health service is in crisis and all the main political parties have said they want to fix it – yet the funding they have so far promised falls well short of the level needed to make improvements.

“Politicians need to be honest with the public about the scale of the challenge the NHS faces and the reality that an NHS fit for the future needs long-term sustainable investment.

“Honesty about this has so far been conspicuously lacking from the general election debate, with both the main parties unwilling to spell out the difficult choices on public spending and taxation that will confront the next government.

“The scenario we have set out is not overly ambitious – it is broadly in line with the pledges set out by the main political parties and public expectations, and assumes the NHS can deliver challenging improvements in productivity.”

The budget for the Department of Health and Social Care stands at nearly £190bn this year – the majority of which goes to NHS England, with just under £30bn going on things like training, public health and buildings maintenance.

On current public spending forecasts, from the Office for Budget Responsibility, the health budget will rise by 0.8% a year above inflation, meaning it will be receiving £8bn a year more by 2029-30.

However, it could be higher if health was prioritised above other areas of public spending, which has happened over the past decade.

The Health Foundation analysis says taking into account changes in the size and health of the population, an extra 3.8% a year on top of inflation will be needed to improve the state of hospital buildings, reduce the backlog in treatment and shift more care into the community.

That equates to a boost in the budget of £46bn a year by 2029-30, leaving a shortfall of £38bn. The think tank said that is based on the NHS becoming more productive too.

The Tories and Labour have only committed to above-inflation rises, while the Liberal Democrats have said they will increase spending by £8bn across health and care by the end of the Parliament.

Health is devolved, so it is up to the governments in Scotland, Wales and Northern Ireland to decide how much to spend on health from within the money available for public spending, which is largely determined by the Westminster government.