David Cameron will today give his support to the use of "drunk tanks" – mobile police cells to hold intoxicated revellers until they sober up.

The Prime Minister will also hint he favours a minimum price for alcohol as he discloses that the cost to the health service of treating drink-related problems has reached almost £3bn a year.

Mr Cameron will seek to focus on the growing damage from alcohol abuse, disclosing that it cost the health service £2.7bn last year, including £1bn on accident and emergency services.

He will back such initiatives as "drunk tanks" – one-person cells used to hold troublemakers – and "booze buses" that tour the streets helping incapacitated drinkers. Mr Cameron will say that in the past year there were 200,000 hospital admissions with patients suffering alcohol-related conditions – 40 per cent more than in 2003 – while the number of people treated for extreme drunkenness more than doubled to 18,500.

He is known to be attracted to proposals under which the sale of alcohol below between 40p and 50p a unit would be banned. Downing Street is examining Scottish moves to outlaw its sale below 45p a unit, as well as a plan to link taxes on drinks to their strength. An announcement is due within weeks.