Denmark Street is great for window shopping but prices in most (not all) of the guitar shops there are inflated. There's only one specialist bass shop there where you might find an EUB.
£600 will buy you a new EUB from Gear4Music in York - but save your money as it is a crock o'cack. I bought a battered, shopsoiled one with bits missing on eBay for around £70, and was glad I didn't pay a penny more for it.
Anything new at that price is going to be a mass produced far eastern product. You might find something functional - but it ain't going to be pretty or refined unless you do some work on it.
Your best bet with a six hundred quid budget is to buy privately and secondhand. Ebay is your friend - and be patient.
Actually, the most bass you'll get for that budget is the one you build yourself, but that's another story.
I don't mean to be a doom & gloom merchant, but I think you need to be realistic. Most Talkbass contributors live on the colonial side of the pond, where there is seemingly a bigger market and more choice. Conceivably, $900-1000 might buy you something OK over there, but it is going to be trickier in Blighty.
Good luck.
Adrian