Canada's top court has refused to hear an appeal to stop the controversial cull of hundreds of ostriches at a farm in British Columbia, leaving the farmers with few legal options to prevent it.

The cull was ordered by the Canadian Food Inspection Agency (CFIA) late last year after two birds tested positive with the avian flu, following an outbreak that killed dozens of the animals.

Universal Ostrich Farms has fought the order since, and the case has attracted international attention including from senior White House officials who have criticised it as an example of government overreach.

The Supreme Court of Canada's decision means the cull can now legally go ahead.