Specifically, no iPhones or iPads.
But ... someone did. Video of part of her performance has already appeared on YouTube.
On her website prior to her epic 22-night, barefoot stand at the Odeon, the 56-year-old singer - best known for "Wuthering Heights" and "Running Up That Hill" - begged her fans to leave their phones off during the show:
I have a request for all of you who are coming to the shows :
We have purposefully chosen an intimate theatre setting rather than a large venue or stadium. It would mean a great deal to me if you would please refrain from taking photos or filming during the shows. I very much want to have contact with you as an audience, not with iphones, ipads or cameras. I know it's a lot to ask but it would allow us to all share in the experience together.
The "Bush iPhone ban" request sparked a national debate in Britain about the generation of people who grew up with mobile devices and whether you can really be "present" or "in the moment" if you're constantly trying to film or photograph what you're doing. Artists have complained repeatedly about fans with phones.
The Guardian reported that her fans strictly adhered to Bush's request and no phones were to be seen.
But singer Lily Allen couldn't resist - she even published a photo from the gig on Instagram.
Someone else went even further. Here, for those of you who couldn't get tickets, is what Bush looks like 35 years after "Wuthering Heights" - a hit when she was 19 - at the Odeon last night, singing "Cloud Busting":