You might be lucky and pick up a secondhand 80s or 90s MIJ Squier for £200. In fact I might be persuaded to part with a Silver Series Precision for £200 as it doesn't do anything that my main precision does already.
SGC Nanyo Bass Collection usually go for less than £200, which is a crime.
If you can find one Peavey Fury basses sell for next to nothing - I bought one from Flat Eric for £165!! - they are great, USA built and classic P bass shape/sound but with skinny Jazz neck. Skinnier, actually.
OLP MM copies sell for not much and are reckoned to be pretty good, although I have never actually even picked one up.
But a decent Westone Thunder is hard to beat.
Edit - I often play and gig with basses that cost under £200. No-one notices or cares.