Too many people in Britain are drinking in the last chance saloon.

Figures released this week revealed a 25% rise in alcohol-related deaths from liver disease in England. In Scotland, where average consumption levels are markedly higher, liver cirrhosis mortality has jumped by 450% in three decades. Around 16,000 Scots a year receive fixed penalties or warning letters for alcohol-linked anti-social behaviour. Growing numbers of intoxicated children end up in hospital. Concern about binge drinking is driving the Scottish Government's legislation on minimum alcohol pricing, which returns to Holyrood next month for second reading.

Now David Cameron has come around to the same way of thinking, which is surprising in a politician instinctively averse to anything that smacks of "the nanny state". Indeed some Tory ministers, notably Health Secretary Andrew Lansley, have been dragged along this path reluctantly. Perhaps he should start visiting accident and emergency departments on Friday nights.

The Scottish Government should not merely welcome the Prime Minister's change of heart but work with him. The Herald has always maintained that a UK-wide minimum price would be more effective at reducing consumption. Once again it illustrates how the devolved governments can set a bold example, as Scotland's LibLab administration did on smoking in public places.

The level at which the pricing is set will be decisive: 40p would be too low to make a major impact. Conversely, making it too high risks encouraging smuggling, illegal alternative drugs and a return of the dreaded "home brew". Such unintended consequences make a sunset clause a reasonable precaution. The Scottish Government has adopted one, backed by the Scottish Tories, and Mr Cameron would do well to follow suit.

Nobody should pretend price controls represent a panacea when binge drinking is so culturally ingrained and European countries manage to combine cheap alcohol with far lower levels of drunken disorder. Hardened alcoholics and the well-off are price insensitive. Labour is right to argue minimum pricing penalises low income moderate drinkers unfairly but this debate should be about the greater good. Those at the sharp-end of drink-fuelled mayhem – A&E staff and police – have no doubt of the link between price and drunkenness. Labour's proposed ban on below cost sales simply would not make enough difference and would be used by big retailers to exploit small suppliers. Labour is right to protest that minimum pricing will further enrich the big supermarkets but, as is proposed in Scotland, the extra profits can be recouped through the tax system.

The example of Canada, which has had minimum pricing legislation for two decades, suggests that price controls do work, though availability may be just as important.

Britain's alcohol problem is not just about young people "pre-loading" but as they are responsible for much alcohol-linked crime and disorder, minimum pricing is a logical place to start. In the same week that a Tory Chancellor put 37p on a packet of cigarettes, Mr Cameron may not be the toast of the town tonight but this is a brave U-turn and we should applaud it.