I think the whole 'booking fee' lark is a nonsense - they should absorb the costs of admin into the ticket price & leave it at that.
Wigmore Hall is a relatively small hall at around 550 seats, great sound wherever you sit, not really a dud seat in the place. John Gilhooly and his team have pulled the place up by its bootstraps after a period of decline, with inventive marketing and the Friends scheme, so that most concerts are over-subscribed, even as the prices rise. Many concerts are sold out before the general public gets a sniff of a ticket. Some musicians are even persuaded to repeat programmes because of demand for tickets.
They would be foolish to 'cheapen' the 'brand' that they've so carefully created (hello Eudamonia!

). Unfortunately it means that ordinary punters like thee & me, Cellini, are often priced out
There is a solution but it means shelling out £200+ to become a really 'special' Friend. Over the course of a year, that might be worthwhile if you've got £200 to spare.
Which is why the BBC's broadcasts from there are so valuable
