Just to report that today I screwed up all my courage and attended the Friendly Spider Programme at London Zoo.
It was FANTASTIC 
I really recommend it to anyone with a spider phobia. It was very emotionally wearing, and lots of the participants were in tears at various points, but everyone handled a spider by the end. I let a house spider run over my hand and also held a tarantula (tbh, the house spider was worse - more jittery - the tarantula was like a gerbil with more legs). First time I have EVER touched a spider, and I never thought I would be able to.