In the last Parliament the then minority SNP Government failed to push through legislation setting a minimum unit price of alcohol to tackle the scourge of high-strength, low-cost alcohol such as large bottles of own-brand cider. An "indicative" figure of 45p per unit has been suggested, which would affect some ciders, wines and possible own-brand blended spirits.

Now, with a majority capable of pushing through legislation, the Government has returned to the issue and the legislation was approved by committee this week, but with Labour and Conservative members continuing to voice disquiet.

With the Liberal Democrats having already switched sides, the Tories announced they had secured agreement from the Health Secretary for an amendment at Stage 2 of the bill to impose a five-year "sunset clause" requiring the legislation to be reviewed after that period.

Because the Scottish Government is convinced of the legality of what is proposed, it has argued it has no need to notify the European Union of what is planned, but ministers have now also agreed to a process of "voluntary notification".

Tory leader Ruth Davidson said: "Support for alcohol minimum pricing represents a major policy shift for the Scottish Conservatives. It follows my commitment as leader to undertake a widespread review of policy and reflects our strategy of seeking to improve Parliamentary bills in the face of an SNP majority at Holyrood."

She said voluntary notification by the Scottish Government to the EU of its proposals will reassure the Scottish Parliament the Government has done "all it can to establish the legality of alcohol minimum pricing ahead of implementation".

The Tory leader added: "While we retain our scepticism, with the security of a 'sunset clause' we have resolved to give minimum pricing a chance to succeed. If it works then we will be delighted we aided that success. If it fails then we have secured the mechanism by which it can be dropped."

Ms Sturgeon said: "We wel-come this support from the Scottish Conservatives who have now added their names to the list of doctors, nurses, academics, politicians and growing numbers of the general population who recognise the harm alcohol is doing to our communities and the benefit minimum pricing will bring – saving lives and reducing crime."

She added: "I firmly believe it is far better for political parties to reach consensus on public health policies. Tackling alcohol misuse is one of the most important public health issues Scotland faces and a consensus across the Parliament shows how serious we all are in our bid to reduce the damage alcohol is doing."

For Labour, Dr Richard Simpson insisted his party remained "absolutely determined to tackle Scotland's drink problem" but did not believe this legislation was the answer.

"It will deliver a multimillion windfall for big supermarkets without providing a single extra penny for our police or the NHS, it will not target problem drinks and big questions remain over whether these plans will be struck down in the courts," he said.

The Scotch Whisky Association said the referral to the EU did not go far enough and the sunset clause was irrelevant if the legislation breached the law.

A spokeswoman said: "The association is pleased the Scottish Government is moving towards notification of minimum unit pricing to Brussels, but noted the discrepancy between the Conservative's request for notification of the bill and the Government's undertaking only to notify the price."

She said minimum pricing had consistently been ruled in breach of EU and international trade rules and the Government's proposals needed to be scrutinised in their entirety.