The head of Lesotho's prosecution service said he intended to charge Balfour Beatty, Kier International and Jacobs Gibb.
The three were part of consortiums that won work from the Highlands Development Authority in Lesotho, a kingdom entirely surrounded by South Africa. The authority was the government body responsible for building a series of dams.
LL Thetsane, Lesotho's director of public prosecutions, said: "We intend to proceed against Balfour Beatty and the other British companies. It is a question of who comes next."
Thetsane said the proposed bribery prosecutions were "among the most expensive cases the kingdom has ever undertaken". He said the only factor delaying the prosecutions was a lack of money, but added: "We will pursue the companies to the bitter end."
Balfour Beatty and Kier said last week that neither had been charged. A spokesperson noted that previous charges against the consortiums had been dropped. Jacobs Gibb declined to comment.
Masupha Sole, the Lesotho development authority's former chief executive, was jailed for 18 years on Tuesday for accepting £3m in bribes over a 10-year period beginning in 1988.
Canadian consulting engineer Acres International is on trial for bribing Sole. The prosecution will make its final submission next week.
A prosecution is pending against French contractor Dumez, and German consulting engineer Lahmayer International is expected to go on trial in August.
The consortiums were first charged with bribery in 1999, but the case was dropped after they claimed that, as consortiums, they "had no legal personality" and therefore could not be prosecuted.
Thetsane said: "For us to have previously tackled these companies shows there is prima facie evidence against them."
If the accused companies are convicted they can expect to be added to a blacklist of firms banned from projects financed by the World Bank and the European Union.