The environmental group tried unsuccessfully to argue that the importation of the cargo was illegal because it contravened the Convention on the International Trade of Endangered Species (CITES) which Britain has signed.Greenpeace had been seeking a judicial review and an injunction to stop the cargo being traded until the court case was over.
The Brazilian government banned the logging, transport and trade of mahogany last October after finding that 70 percent of the timber was being logged illegally. It also found that large amounts were coming from protected Indian lands.
Campaigner Andy Tait said of the decision: "In essence the judge said that the export permits concerned are valid, otherwise they would not have been signed by the relevant management authority."
The management authority in this case was the Brazilian Environment Agency, IBAMA.
"Whether or not that decision (to allow limited mahogany exports) is under appeal in the Brazilian courts is not a matter for the UK," he said.
Tait said that IBAMA was forced by local Brazilian courts to allow limited exports by companies that could show they had logged the timber before the trade ban.
"We are considering appealing on the grounds that we believe at the very least there is an arguable case that this mahogany and other shipments like it should be stopped from entering the UK while checks are made that it conforms to the CITES convention," he added.
The 811 cubic metre cargo aboard the ship MV Cunene is moored at Birkenhead docks, near Liverpool.
The importing agent in Britain, Alan Thomas Craig, declined to comment on the case.
Greenpeace said Britain is the third largest importer of Brazilian mahogany, which is used to make furniture, musical instruments, window frames and coffins.