The Joie Stages does convert to a high backed booster mode up to Group 2, so they could convert that and keep using it. However IMO it doesn't give that good of a fit, so if they are happy to get another seat then that would also be a good idea - it would also last all the way rather than needing to be replaced at a later date.
In terms of the 25kg harness seats you do have Cozy n Safe Hudson (NOT i-size) and Enfasafe Event FX, both of which are sub £100, but they do need isofix, seatbelt and top tether to fit, and TBH with her stats, unless there are behavioural issues making you lean towards harness, I would say she'll be better off in a good HBB seat than a budget harnessed seat.
But a good HBB for up to £100 is easy 
And if you can hold out until May bank holiday weekend that is normally a sale.
Joie i-Trillo
Graco Eversure i-Size
Britax Adventure Plus 2
Cybex Solution B4 i-Fix
Cybex Solution X i-Fix
Maxi Cosi Rodifix M
Maxi Cosi Tanza (prob not the folding one - unless you want a folding one?)
If you do look in sales:
Anything Cybex, Maxi Cosi, Recaro, Britax or Joie is fine.
Some other notes:
Some of the very old options by Maxi Cosi or Cybex are looking a bit dated now - if you're looking at deals online, try to check the date of manufacture/release. As a rule of thumb, with car seats, newer = better because it will have better technology. Britax is an exception, because an old Britax is often as good or better than a modern anything else. I did see a couple of old Joie Trillo (not i-Trillo) in stock - would steer clear of these as you have so much choice of newer ones.
I'd be wary of Graco, as they have some great items and some questionable ones especially in boosters. The Graco R129 booster seats with the same head shape as Joie are likely good budget options, but they aren't yet ADAC tested, so if you have a higher budget, go higher.
Britax Adventure/Discovery Plus had a minor/annoying fault that the headrest can easily break. No recall because if it breaks it's obvious, they basically replaced it ASAP with the "Plus 2" versions. Some shops still have the older "Plus" version in stock - avoid this, because dealing with an online customer service thing for returns/repair on the fault is annoying.