Hey Peach, I love the one at Broadgate Circus, just at the back of Liverpool St station, 100 bus.
You can hire skates, the rink isn't enormous but larger than some of the popup rinks.
The one at Canary Wharf is good too but go early at weekends.
You do get the show offs whizzing round skating backwards but at no risk to us edge huggers. There's a nice bar also for afterwards and reasonable [by City standards] food. Chaotic when the kids break up but they all are but Broadgate Circus not to chaotic as the one at Somerset House in the Strand, now that's larger but one to avoid in my opinion.