Homelessness charities fear that the London mayor, Boris Johnson, has skimmed off more than £5m of government funding intended to help rough sleepers and diverted it to other purposes.

The cash has gone missing from Johnson's budget for support for rough sleepers, which is wholly underwritten by Whitehall. Repeated efforts by the charities have failed to win assurances that it will be restored.

At a time of rising homelessness, services for people sleeping on the streets of the capital face cutbacks or closure if the money is not reinstated.

The government has transferred a total £33.8m to the London mayor to fund services for rough sleepers over four years to 2015. The allocation equates to almost £8.5m a year.

In 2011-12, the first year of the programme, spending amounted to £7.5m. Although the mayor says he plans to make good the underspend by committing £9.5m in 2012-13, his budget states that he will be investing a total of £21m across that year and the remaining two, making a total of £28.5m.

This implies sharply reduced expenditure of less than £6m in each of the two latter years of the programme, after the Olympics spotlight moves away from London, and an overall underspend of £5.3m.

In a joint letter to Johnson, which has been seen by the Guardian, charities providing pan-London services for rough sleepers say the figures indicate a "clear cut" of 16% in the funding entrusted to him to disburse.

"The £33.8m was specifically transferred from central government to be spent on commissioning services that cannot or would not be provided at a London borough level," the letter states. "Cutting those resources can only imply that in future years such services will in turn be ended or their funding cut back …"

Johnson, who is campaigning for re-election on 3 May and has reduced his council tax demand for 2012-13, pledged previously that by the end of 2012 no one would be living on the streets of the capital and no individual arriving on the streets would sleep out for a second night.

To co-ordinate activity, he set up in 2009 a delivery board to bring together work on rough sleeping across London. In recognition of its success, and in line with the government's policy of localism, the Department for Communities and Local Government devolved to him the £33.8m.

The cash was not formally ringfenced for rough sleeping programmes, but Johnson's housing adviser, Richard Blakeway, assured London boroughs in February 2011 that "much of the funding is contractually committed for 2011-12 and the mayor will ringfence the remaining devolved funding to ensure that it is targeted on delivering an end to rough sleeping".

The latest estimates suggest there may be about 700 "entrenched" rough sleepers in the capital, although a survey last summer traced 2,000 people sleeping out on at least one night over a period of three months.

The typical hardened rough sleeper is a man aged 26-45 from outside the UK. Those from central and eastern Europe are now thought to represent at least a third of the total. According to a survey published on 28 March, day centres across the country are seeing 25% more homeless people than in 2010 and rough sleepers constitute the majority of people at a third of all centres.

One service for rough sleepers in danger of losing its funding from Johnson is the Olallo project in Camden, north London, which caters specifically for central and eastern Europeans and has money only until September.

A service that has already lost its funding, as of the end of March, was a small befriending and mentoring project for rough sleepers run by the Christian charity Housing Justice. Over the past two years, the project kept an average 17 individuals off the streets.

Alison Gelder, director of Housing Justice, said: "We were told it wasn't helping the most entrenched rough sleepers and wasn't going to be refunded."

Other charities fear they will hear the same message unless Johnson undertakes to restore the missing £5.3m. In the joint letter to the mayor, dated 21 March, they have asked for written confirmation that the full government grant "will be made available for its specific purpose"; that none of the cash will be used for employment programmes for groups other than rough sleepers; and that the budget will be amended accordingly. They have received no reply.

When asked at a public meeting on 7 March whether the cash would be spent "in its entirety on preventing and tackling homelessness", Johnson replied: "Yes, absolutely." He said: "Of course we are going to spend every penny that we can on dealing with the problem."

Asked by the Guardian whether the mayor would guarantee that the full £33.8m would be spent on support for rough sleepers, Johnson's election campaign spokesman said: "He has committed £9.5m to rough sleeping for 2012-13 and this funding has allowed him to extend the successful No Second Night Out scheme to the whole of London which has helped over 800 people in a year.

"Since 2008, there as been a three-quarters reduction in the most entrenched rough sleepers and 80% of new rough sleepers now spend just one night on the streets. We cannot go back to the waste and neglect of the previous administration and Boris will build on this strong foundation in a second term."