The car's new red livery features the Winfield brand logo and a picture of a kangaroo and objectors say the deal breaches the spirit of Australia's anti-tobacco sponsorship law.
All forms of tobacco advertising are banned, but the law allows exemptions if a major international sporting event such as the grand prix would otherwise be lost.
Dr Arthur Chesterfield-Evans, president of the Non-Smokers' Movement of Australia, said the exemption is intended to allow international events to be unimpeded by local law. "But this sponsorship is against the spirit of the agreement because it is supposed to be for international brands and I believe the government could act to say this is not on," he said.
Chesterfield-Evans also called on the government to tell Williams to drop the Winfield colours for the grand prix.
However, a spokesman for Rothmans, who own the brand, said the deal with Williams was an international one and therefore within the law. "There's an assumption that Winfield is only sold in Australia, that's not the case. It's sold in 13 countries on three continents."
The row over tobacco advertising shows no sign of abating in Britain, either. Lord Hesketh, president of the British Racing Drivers' Club, the owners of Silverstone, said yesterday: "The implications for British motorsport are very bad indeed," he said on the decision to ban tobacco sponsorship in sport. "It's a demented policy. It's bad, cheap, single issue politics and it will cost us jobs."
Motorsport has been given a temporary stay of execution from the ban, which will affect other sports soon after the millennium, but it has been ordered to investigate alternative forms of revenue.
"The effects will be long term. Races will move from Europe to the Far East and it won't take long for people to realise it's cheaper to relocate to where the races are held," he added. "Fifty thousand jobs are at stake here. However, I get the feeling that people will only discover what they have lost when it's gone."Reuse content