Topshop has lost a high court battle with pop star Rihanna in a ruling that could cost the fashion chain £3m.

The American singer, acting under her real name Robyn Rihanna Fenty, sued Topshop's parent company Arcadia for $5m (£3.3m) over the use of her image on a T-shirt last year.

Judge Justice Birss ruled the picture used on the T-shirt was "very similar" to images featured on Rihanna's Talk That Talk album cover and so a "substantial number of shoppers" were likely to have bought the garment believing it had been approved by the singer.

The judge ruled in favour of Rihanna on the basis of "passing off", a legal principle relating to consumer confusion over the status of the clothing. He said the incident marked "a loss of control over (Rihanna's) reputation in the fashion sphere" but made clear that famous people had no "freestanding general right" to control the use of their image. The written ruling said there was no suggestion the taking of the photograph used by Topshop had breached Rihanna's privacy.

Garry Assim, a partner at law firm Shoosmiths who is an expert in image protection, said the only place in the UK celebrities images were formally protected was in Guernsey. "This judgment may reignite the debate over whether there should be formal image rights in English law," he said.

Topshop is to seek permission to appeal. A spokesperson said: "We robustly dispute the judge's conclusion. We believe that our customers clearly understand when we are undertaking a collaboration, such as the one we created with Kate Moss over several seasons."