Does anybody have advice on good equipment for muting/dampening my pianos as I have recently moved into a flat and am having trouble with a downstairs neighbour.
I'd really appreciate any advice, expense is not a concern.

Thanks

First, are we discussing an upright or grand piano?

If it's a grand, take a look at this thread from a few days ago:
Grand piano practice silencer

Also, if price is not a concern, have you entertained the idea of buying a new piano with a practice pedal? Most new uprights have them.

thanks for the link - I have one grand and one upright.
Is the reduction in volume significant? I'm worried the sound will still carry down through the floor.
Really appreciate any tips for this as well.
Thanks!

I have played uprights with practice pedals, but not grands.

Yes, the volume reduction is VERY significant. It's barely loud enough to hear while you are playing. One thing that I didn't really care for is that the muting was not very consistent...some notes were quieter than others. But they definitely do work!

Stop by any piano store and try one out.