I'd definitely be looking at a Xiaomi, Realme, Motorola or Nokia at those prices.
I'll concentrate on Xiaomi as I've been following them closely recently. Depending on size, the Redmi 9 (not small, but the smaller of the two) and Redmi Note 9 are regularly on offer, the smaller around £100 while the larger seems to be around £120. Generally regarded as solid phones and an absolute bargain.
Slightly above them and where I was looking you've got the POCO X3 NFC (seems to be permanently on offer around £160-170 for the 6GB RAM and 64GB storage option and sometimes just £10 more for the 128GB option) and slightly above that the Mi 10T Lite which is a good device just below £200, though occasionally comes down to around £185 for the same storage. The differences between them are slim. The POCO X3 has a slightly bigger battery though a plastic back, while the 10T Lite has a glass back, slightly better processor and 5G. Both have 120Hz displays but LCD rather than AMOLED. I think the cameras are similar.
Personally I went for the 10T Lite and got it for £164 as I used a self-referral method (saved £15 by using a second email address to refer my primary email, which sends a coupon and is applied at checkout if ordered within a certain time). The LCD screen is much better than the one in my previous phone, but isn't always on due to not being AMOLED, the primary camera is excellent for the price (very good especially in good light, less so in poor light), the ultrawide is OK though the macro camera is utterly pointless and is best ignored. I can't comment on the selfie camera. Battery life seems good so far, though I limit the screen to 60Hz. The fingerprint reader (which is on the power button) is extremely quick. The phone has space for two sims or a sim and a microSD card (I think most Xiaomi phones are similar). MIUI is an acquired taste, though coming from a J5 it's probably no worse - Nokia and Motorola would provide a close to stock Android option. I flashed straight to a stable beta of MIUI 12 (don't need to do anything special, just download the file from Xiaomi and flash it in the settings) which brought me onto Android 11. Noticed a few little quirks when setting it up, but nothing major and probably just due to my choice of going straight onto the beta version - in day-to-day use I've not noticed any bugs and stability is certainly fine.
There are adverts on MIUI, usually not intrusive and limited to Xiaomi's own apps or in the settings, but they can easily be disabled by following the instructions
here. You can disable some of the other apps if you won't use them and apparently MIUI 12.5 (scheduled later this year for all of the above devices) will allow you uninstall a lot of the built in apps as standard.
All I will say is make sure you get a Xiaomi from a UK store - either Xiaomi themselves or Amazon or the likes) to ensure you get a proper UK version with full band support. If you want to try the £15 referral direct from Xiaomi (it is shipped from the UK if bought from the UK store) then the link for that is here:
https://buy.mi.com/uk/user/invite. As far as I know it still works and certainly worth a go, though obviously it does mean you'll end up with two Xiaomi accounts, though they aren't needed for anything unless you intend to unlock the bootloader (which you'll almost certainly not do).
I did look at Motorola too and they had some good options, but I think every phone around this price was limited to 4GB RAM and I just thought in the long term 4GB might be a bit limiting. For most users it would certainly be fine though, so worth a look, especially if stock Android is preferred.
