As Ethel states, everyone is liable for income tax. If a businessman puts some shares into his baby's name, the baby is liable to pay tax on the dividends.
However everyone has a 'personal allowance', which allows them to earn a certain amount each year which is free of tax. For most people that allowance is currently �6035 per year (which equates to �116.06 per week). From April the personal allowance goes up to �6475 per year (�124.52 per week).
Students who only work during their vacations generally don't earn enough, in each financial year, to pay any tax. Similarly, young people who deliver newspapers don't earn enough to pay tax. This has led to a myth that students (and young people in general) aren't liable for income tax. It simply isn't true; everyone is subject to the same rules.
If the young person's tax code (on their pay slip) is 603L, they should be paying the correct rate of tax. (Any discrepancies, caused by changing jobs or rates of pay, are automatically adjusted by the tax system). In April, that tax code should rise to 647L
Chris