Parents could be taken to court for letting their child try alcohol at home under proposals being considered by ministers.
Currently children as young as five can drink at home with parental supervision but a Government review is looking at raising that limit.
The Youth Alcohol Action Plan, which aims to curb binge-drinking among teenagers, could also lead to a 9pm watershed for alcohol advertising.
Ministers have already outlined a plan for official guidance for parents on how much alcohol their children should be permitted to consume at different ages.
But if the law is changed parents face the prospect of a fine for giving their child a wine or a beer.
Chief Medical Officer Sir Liam Donaldson will carry out the review, which will consider what age is suitable for children to start drinking, how much they can safely drink and to what level the drinking should be supervised.
Sir Liam said: 'The law at the moment says that you mustn't give alcohol to your child under five.
'We are going to look at the evidence very systematically and see whether it needs to be changed or strengthened. In the past, getting drunk was a rite of passage for young people.
'But over the last decade or so we have moved to a situation where it's more than a rite of passage.
Children's Secretary Ed Balls said the drinks industry faced further advertising restrictions.
Drinks manufacturers and retailers are also likely to be forced to meet a strengthened set of 'social responsibility standards', compelling them to promote responsible drinking and to ensure that no under-18s buy alcoholic drinks.
It will also introduce tougher powers for the police to disperse gangs of youngsters congregating in the open, including a new offence covering the persistent possession of alcohol. Shops caught selling alcohol to children face a 'two strikes' rule.
The City of London Corporation claimed the advent of 24-hour drinking had led to a surge in yobbish behaviour.
Tory home affairs spokesman James Brokenshire said: 'Yet again the Government mistakenly think that new laws are the answer.
'The problem is that they can't even enforce the ones they've already got.
'It's breathtaking that even now they accept no responsibility for the consequences of the way they introduced 24-hour licensing.
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