The World Bank has accused western countries of hanging on to billions of dollars in fines involving corruption cases in developing countries.

An investigation of almost 400 cases over 13 years found that about $6bn (£3.7bn) was paid by the companies concerned, mostly in out-of-court settlements. But only 3.3% has been returned to the countries whose officials took the bribes.

In Left Out of the Bargain, a report released on Wednesday, the Bank points out that the overwhelming majority of countries that paid over the odds for roads, dams or bridges were in developing countries. Most of these deals involved state contracts, ranging from tens to hundreds of millions of dollars.

There has been a growing trend over the past decade to use settlements to conclude foreign bribery cases rather than go through full trials. The World Bank concludes: "In the majority of settlements, the countries whose officials were allegedly bribed have not been involved in the settlements and have not found any other means to obtain redress."

Tim Jones, of the Jubilee Debt Campaign, described the fact that such a tiny sum of money had been returned as "outrageous". "Governments, especially of financial centres such as the UK and Switzerland, need to be doing far more to find and seize corrupt and stolen money, and make sure it is returned to the people affected," he said.

Speaking off the record, officials say the reason why so little of the money has been returned is because governments in the developing world have shown little interest in pursuing corrupt officials. It has been left to Britain, Germany, Switzerland and the US to levy the fines, to ensure a more level playing-field for their own companies.

The report makes no mention of how much each western country has retained of the money that has been received, but the World Bank's Stolen Asset Recovery Initiative is launching a website to allow these calculations to be made.

Nineteen British companies are named in the report, including some well-known exporters. The construction firm Mabey & Johnson was caught paying bribes to Iraqi officials in a major bridge construction project, as well as making corrupt payments to officials in Ghana and Jamaica. In 2009, Mabey entered into a plea bargain with the Serious Fraud Office and was ordered to pay £658,000 to Ghana, £139,000 to Jamaica and £618,000 to Iraq. Payments have been made to Iraq and Jamaica, but no transfer of funds has been made to Ghana.

Macmillan Publishers are also named as having reached an agreement to pay £11m to three African countries in which they were involved. Perhaps the best known settlement was reached by BAE, which repaid £29.5m to the Tanzanian government, after supplying a radar system with military capabilities far beyond the needs of the country.

The World Bank is launching the report in Panama, where 1,500 delegates of the UN Convention Against Corruption are meeting. Jean Pesme, co-ordinator of the Stolen Asset Recovery Initiative, hopes the startling lack of money returned to developing countries will persuade them to join prosecutions brought in London, Washington or Zurich.

"If you are a developing country, you can be a party to a case," he said. "In our view, the effected countries should be allowed to join the prosecution."