Our employer asks us to turn up 15 minutes before work starts, but don't pay us for this time. Shouldn't this come under our paid time?

You should check your contract to see how your paid time is defined. It may be mean, but it would strictly be legal for your employer to offer you a contract that includes unpaid time, so long as your total pay (excluding non-contractual overtime) is at least as much as the national minimum wage for the full hours you do work.

For example, as the adult rate national minimum wage is £5.73 per hour, the legal minimum for an 8 hour day would be £45.84. If your employer also insists that you be there for another 15 minutes then they must be paying you at least £47.27 per day (£5.73 x 8.25 hours).

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 the employer's premises, and have been very successful in negotiating things like paid tea breaks and, more recently, payment for on-call time spent at work.