Thank you so much for your patient responses!
I probably should have spoken a little bit about what I'm currently using. I've always been a stock Fender kind of guy... used to own a P-bass, then a Jazz, and now I use a Jaguar mainly. For what it cost me a few years ago it's surprisingly versatile - I don't use the on board pre-amp much, if at all these days as I have a Lehle Basswitch with a 4-band parametric EQ, and together with the series / parallel switches on the guitar I can access lots of different 'nice' tones. Enough to get me by I suppose, but I've just outgrown it in the last year.
I'm using flats at the moment as opposed to roundwounds, which are fantastic for a lot of the stuff I play but do compromise in areas where I need greater amounts of sustain and/or attack. The problems I have with the Jag are the following: Only 20 frets on the neck, its 30" scale which means the strings are sort of close to being flabby (I'd say more 'non responsive'), it's only got 4 strings, and finally it just generally sounds a bit flat and dead, unless I'm playing the hell out of it.
Let me also clarify some of the points I made in the OP. I am mortified at having to spend anything close to £4/5000, I would of course prefer to spend less and am well aware that I could get something decent for half that budget, BUT I have perhaps wrongly come at it from the perspective of this being a long-term investment, and with a lot of research and testing (yes I agree!) I can't imagine choosing a guitar that I later regret massively. But maybe I'm just being naive. A trip to Bass Direct is definitely in order! That was always the plan - if I have the opportunity to play a Ken Smith for example before parting with several thousand pounds, then I'm going to jump at it, of course. But with other basses that could potentially come into the top end of my budget - Mattisson, Fodera for example - I just don't have that opportunity for a play before you pay.