Right now, a lot of British people feel quite protective of the NHS. They see it as a scarce and precious resource that should be used sparingly. Many people feel a real sense of guilt if they inadvertently miss an appointment, because they feel that they're taking something away from someone who might need it more.

Converting this reciprocal relationship to a transactional relationship is very risky. Many people who would otherwise make an effort to keep their appointments could take the attitude that they're just paying for a service; the lost deposit takes away any guilt about missing the appointment. £10 is a fraction of the actual cost of a missed GP appointment, so the NHS could make a substantial net loss.

I think a far more productive approach would be to use behavioural nudges. It wouldn't be difficult or expensive to give an SMS or automated voice reminder of an appointment. People who persistently miss NHS appointments could be offered support in keeping to their appointments, while being gently reminded of the costs to the NHS and the effects on other patients. I suspect that a bit of psychological carrot-and-stick would be far more effective and far less risky.