You must be paid at least the National Minimum Wage for all the hours when you are working. This includes all the time when you are required by your employer to be at or near work (other than at home) for the purpose of doing work.
Since you are required to turn up 15 minutes before work starts, this is working time, for which you should be paid. However, your employer will not be breaking the law if, under your employment contract, you are paid at least the National Minimum Wage for all the hours you spend working, including the 15 minute early start.
As long as you are paid at least the National Minimum Wage, whether or not you are entitled to extra wages for the 15 minutes before work starts will depend on what your contract terms say. You should check your contract to see how your paid time is defined.
In addition, the extra time will count towards the 48 hour average limit set by the Working Time Regulations. Most employees can't be made to work more than this unless they want to. If there's a union where you work, it will be worth checking with them, as trade unions make it a priority to ensure workers are paid for all the hours they have to spend on their employer's premises.
They have been very successful in negotiating things like paid tea breaks and, more recently, payment for on-call time spent at work.
Trade unions make it a priority to bargain for workers to be paid for all the hours they have to spend at their employer's premises, including exactly the sort of scenario you describe. If you are not a union member, browse our Union Finder tool to find out which union best suits your needs, and to discover more about organising to secure union recognition at your workplace.