Two obvious considerations:
1. Have they decided if they want an upright or grand?
2. Do they have a strong preference for new or something older? Some people have strong preferences for what will look best in their house!
If they are shopping for an upright, that is a great budget that will give them a really wide choice of fine instruments old and new. Any of the good piano shops will only sell you something good at that price - you won't get a liability that will need lots of repairs in the future. So you have freedom to simply have fun trying things out and going for what suits you best. Good shops that immediately spring to mind in London are Jacques Samuels, Peregrine's and Markson pianos.
As a matter of curiosity, it's interesting to try second hand pianos in the price range that might be on sale in these shops. The style of piano and sound is often very different to modern instruments, so it's a matter of personal preference, but at that price you could get something really wonderful second hand. It's down to luck with that though - older instruments are very individual and you never know what you might see. Buying an older piano from a top shop isn't much of a risk - they will always ensure the pianos are in great condition, and in some cases will have reconditioned them, but it's rare to find an older piano that holds its tuning as well as a brand new instrument, so anyone buying one needs to be prepared not to skimp on regular tunings.
For new instruments, I would second the Kawai recommendation. It's worth a visit to Jacques Samuels as they have many Kawais, but also specialise in Hoffmann pianos - also very worth trying. A little known make that I like is Venables, but you can only buy them from Venables Pianos in Ringwood, Hampshire.
Mainly though, at any good shop, try as many new pianos as you can in the price range. Each piano is a bit different from each other as well, so the more you can test, the better.
One thing worth considering is covid piano testing rules. Presumably, piano shops will be on an appointment only system for now. It's worth checking if they limit the number of pianos you can test. That's fine if you kind of know what you want, but if you want to test as many as possible, it might be worth waiting until rules relax more before shopping. That may not be an issue - they may let you test as many as you like, but I think it's worth checking before you go.