The city of Bath is planning to lobby the government for the power to charge its many visitors a tourist tax.

A levy of about £1 or more could be added to the accommodation bills of the million or so tourists who stay in the Georgian city every year.

Councillors see it as a way of raising extra cash in times of austerity, but many hoteliers are reluctant to charge tourists, believing even a small additional cost will put off some visitors and claim such a scheme would be difficult – and expensive – to administer.

Bath has long considered raising a tourist tax but had previously been told by Westminster it would not be allowed to.

After it emerged at the end of last year that Birmingham might be given the go-ahead to impose a levy on visitors to help pay for the 2022 Commonwealth Games, Bath decided to revive its plan.

The council leader, Tim Warren, said: “We believe that considering the numbers of visitors we get in Bath a small fee for overnight stays is the way forward. This would go to service the tourism budget and funds that would have usually been diverted there would be free to be put to use elsewhere.”

The Liberal Democrat councillor Dine Romero said: “Most residents will think this is a good idea. But it would be a real worry for the bed and breakfast level of establishments in the city because a pound here and there does make a difference in that market to whether people choose to stay there.”

Robin Moss, a Labour councillor, said: “Most European cities have it. I don’t think it would affect tourism but bring in much-needed revenue.”

About 5 million daytrippers come to Bath every year and tourism supports about 10,000 jobs in the city and surrounding areas.

On the streets of Bath on Wednesday, most visitors seemed happy with the idea. “I could afford another pound or two,” said Frank Cooper, who was on holiday from the US. “It wouldn’t put me off. I can see that visitors put a lot of strain on the city.”

Last year, the film director and Bath resident Ken Loach caused controversy when he told the Guardian the city was being ruined by unsympathetic developments intent on attracting even more visitors.