The activists said the EIA misrepresented the site's geological makeup, and downplayed the threat to endangered species and the risk of catastrophic flooding if the dam burst.
An Amec spokesperson said the firm stood by its EIA, which was completed earlier this year.
The £18m dam is being developed by Canadian utility firm Fortis to generate 5.3 MW of electricity – about 10% of Belize's requirements.
There is a risk the dam will cause serious environmental damage
Bacongo lawyer Richard Clayton
The Belize Alliance for Conservation Non-governmental Organisation (Bacongo), an international coalition of organisations opposed to the dam, has failed in five legal attempts to stop the project. Following its defeat in Belize's supreme court in June 2002, it appealed to the Privy Council, the final court of appeal for Commonwealth countries.
On Wednesday, Bacongo asked for a temporary halt to work on the site, pending the Privy Council ruling.
In his submission to the court, Bacongo's lawyer, Richard Clayton, said: "The construction work has seriously adverse effects. It may be catastrophic. There must be a substantial risk that it will have profound effects and very serious environmental damage."
Clayton pointed to the environmental effect of the nearby Mollegon dam, which caused slime and sediment to build up in the Macal river.