For that budget and in the UK, a decent mid-20th century European laminate bass could be a good choice, and they do come up if you wait around and watch on here and other bass specific selling places. Or relatively recent carved or hybrid student basses like the Stentors, Zellers, and Czech and Romanian ones under a few names would also be good.
Any older carved bass in that range will likely have something keeping the value down, perhaps less than ideal old repairs, or needing immediate work, but you might just get lucky.