Legal disclaimer - I'm not a lawyer........
Here goes:-
Wildlife & Countryside Act 1981.
Section 16 - Power to grant licenses:-
(5) ©may be subject to compliance with any specified conditions;
Taken from Wildlife & Countryside Act 1981
Its my interpretation (reminder - get legal advice, not internet heresay!) that the above gives those who issue the license(s) the power to add specific conditions.
The question remains is would a judge consider flash photography, based on no (that I am aware of) scientific research or grounds, consider the restriction 'reasonable'? And would anyone want to actually test this in court? Two questions, one answered with 'who knows?' and the other with 'unlikely to never'. Wetpixelers can make their own guesses as to which answer goes with which question.....
Plan B - Paul's 'appealing the ban' - appears to be the least painless option.