White Waltham
Avia Special are one of the companies that offer Tiger Moth flights from White Waltham but I believe that there are others as well.
Avia can be contacted on 01707 378581. I believe that they are fairly photographer friendly as there are always plenty of people with cameras over there.
It may be worth finding out exactly which company he is flying with.
White Waltham in general is very accommodating of photographers.