as an aside, £3-400 is considered mid-range these days. top-end is ~£1k and up, i'm afraid!
i'd probably try to get something that's a couple of years old - the last few years haven't seen much in the way of major improvements to phones other than the folding screens, and those are still a bit too early-adopter for my liking (and ~£2k, too). huawei's p30 was fantastic, but was the last to support google's apps - i've held off upgrading from mine because if you stick a wireless charging case on it then there's really nothing else out there that isn't an incremental upgrade at best. those go for around £150 or so on ebay second hand, which is an absolute steal. my kids are still using our previous honor 8 and honor 9 phones happily (10/12 years old) although the eldest dropped hers so she's basically waiting on one of us to upgrade to have our p30.
google are soon to release their new pixel 6, which might be worth looking at, too (although expectation in price terms is likely to be £7-800, I suspect). if not, their previous versions are really good for the money and will get very good support. i probably wouldn't get anything older than a pixel 4, though.
at the really cheap end of things, motorola's g-series and the oneplus nord are really good phones for not much money.