Hello Scarlett, it's been a long time ;o)
Yes, there are all kinds of things that can be fixed to a ceiling, but that would only do half a job.
It would help to deal with "airborne" sound, but your problem is mainly "impact" sound.
Separation is the best way to deal with that... i.e. fixing a suspended ceiling away fro the existing. The new ceiling would have to be of a fairly high specification (airborne sound).
I must say it would be quite expensive, and disruptive though.
In my experience of flat conversions, this does in fact come under strict Building Regulations rules. I guess this building was converted some time ago.
One long shot ... in one conversion I was involved in, the lease held a covenant forbidding bare floors in flats "above". Worth checking this.
A bit heavy-handed, I know, but Environmental Health should be told. I wouldn't hold out a lot of hope that they would act, but it may be a last resort.