I've just had a call from my GP surgery letting me know that I'm at the top of the list for counselling and they have an appointment available for me next week.
The counsellor is only at the surgery on one day of the week and I finish work at the same time as the slot starts. She says that they should give me the time off but I don't really want them to know why I need the time off.
Would they need any more information other than the fact it's a medical appointment?
That's up to them really. If you want them to pay you then it will depend on any policy they have on paying for medical appointments, which might include needing to see an appointment letter or similar.
If you have a reasonably sympathetic supportive manager, then saying you have a medical appointment but its a private matter will probably be enough, but you are not legally entitled to paid time off for it so you are in the hands of your employer really.