The last time I was in London one could not climb past the whispering gallery. Traveling with an 8 year old, and "the climb" would probably be the reason to take her.
https://www.stpauls.co.uk/history-collections/history/explore-the-cathedral/climb-the-dome#
Looks like you can go all the way to the top.
Thanks for the link
I'm hoping somebody will have been there recently. 18 months ago I took my two tween boys there and discovered we couldn't get past the whispering gallery for some reason.
We were at St. Paul’s last July. We definitely climbed up the dome. It was definitely higher than the whispering gallery, I believe it was to the top.