Charities have sounded the alarm over the way ministers are spending the multibillion-pound aid budget, saying some is being diverted from the poorest countries to promote commercial and political interests.

In a letter to the chancellor, Philip Hammond, which has been leaked to the Observer, 23 agencies warn that some aid is no longer being used “effectively and efficiently” and that taxpayers “are not getting maximum value for money”.

It marks a shift in tone from the agencies, which have been reluctant to suggest that aid has been directed to the wrong projects. However, with the government obliged by law to spend 0.7% of GDP on aid, there are concerns that ministers are finding ways of classing politically convenient projects as aid – and attaching strings, such as cooperating with British industry.

Save the Children, Oxfam, Action Aid and Christian Aid are among the charities that signed the letter. They call for Britain “to be seen to be implementing the spirit, as well as the letter, of internationally agreed rules”.

“In a changing world, there are good reasons for different government departments to spend aid,” the letter says. “However, we are concerned that not all UK aid is being spent effectively and efficiently and that this means that UK taxpayers are not getting maximum value for money from every pound of aid.

“Value for money is best achieved when aid programmes are results-focused and are not tied to goods and services from the UK. However, several departments are failing to clearly identify the results of their aid programmes and some aid spending appears to be de-facto tied. Of the aid spent outside DfID [the Department for International Development], over a third is spent in upper middle-income countries, which have little need for aid.

“In the context of increasing public and media scrutiny of the aid budget, it is important that we can clearly demonstrate to UK taxpayers that aid is being spent in line with their own priorities and to help the most vulnerable.”

A committee of MPs raised concerns last summer over aid delivered under the Prosperity Fund, run by the Foreign Office. They said its focus on promoting British trade was a “step towards” tied aid. Projects supported by the fund included development of the film industry and improving museum infrastructure in China.

Meanwhile, the cross-departmental Conflict, Stability and Security Fund was used to build a £700,000 jail wing in Nigeria, allowing foreign criminals to be deported and freeing up places in British jails.

The latest intervention comes with signs that both the size of the aid budget and the DfID itself could be under threat. Figures including Boris Johnson, a frontrunner to replace Theresa May as Tory leader, have suggested DfID should be folded in to the Foreign Office. Penny Mordaunt, the international development secretary, has questioned Britain’s pledge of spending 0.7% of GDP on aid.

A spokesperson for DfID said: “Reducing extreme poverty, hunger and providing clean water and sanitation are at the heart of what UK aid does, but our investment is also about tackling disease, climate change and drivers of terrorism and conflict, combating global challenges while also working in the UK’s national interest.

“The delivery of aid programmes by departments other than DfID has enabled the UK to leverage knowledge, skills and expertise from across government.”