It should be raised to something like £250,000 IMO, inflation doesn’t stop. Should future proof it for a while (or maybe even link the deposit limit to inflation and start at this adjusted figure).
The BoE should have simply kept it circa €100,000 (circa £87,500) to stay aligned with the EEA and ready to promptly re-join the EEA.
Why do you think £120,000 is incompatible with the EEA? To begin with, there is no party interested in having that conversation now (or probably in our lifetimes, regrettably, unless the 4 Freedoms are renegotiated, which isn’t negotiable, we tried). Secondly, these rules introduced by EU institutions set minimum standards, nothing stops anyone from going above and beyond.
Besides, it’s been the EU limit for a good while now so chances are it’s going up soonish to maybe €150000 which ain’t too far away from that £120000.