Well, I feel like browsing, so I thought it would be nice to compile a list of the various online shops selling vintage and used basses in the UK, or indeed the EU. I'll add your suggestions to the original post. Here's the list so far, in alphabetical order:
The British Isles:
Absolute Music (Bournemouth)
Andy Baxter (London)
AngelDust (Multi-location?)
Bass Direct (Warwick/Leamington Spa)
The Bass Gallery (London)
Charlie Chandler's Guitar Experience (Hampton Wick)
Classic and Cool
David J Pym (Hungerford)
Guitar Classics (London)
Guitar Village (Farnham)
Jimi's Music Store (Dublin)
Live Music (Edinburgh)
London Vintage Guitar/Hanks (London)
Lucky Fret (London)
Mansons (Exeter)
Mudpie Music (Brighton)
The Music Locker (Ripley, Derbyshire - by appointment only)
Nicks Guitars (Wetherby)
New Kings Road Guitars (London)
No.Tom (London)
Oasis [Musical Instruments Ltd] (Ringwood)
Promenade Music (Morecambe)
Really Great Guitars (Ombersley)
Rich Tone Music (Sheffield)
Some Neck Guitars (Dublin)
Strung Out Guitars (Glasgow)
Tommy Twang's Guitars (Glasgow)
Vintage and Modern Guitars (Thame)
Vintage 'n' Rare (Bath)
West End Music (Ipswich)
Wunjo Guitars (London)
Continental Europe:
Bass Classics (Somewhere in the Netherlands)
Bass Club Paris (Paris, France - can you believe it?)
Bass N Guitar (Somewhere in France)
Guitare Collection (Paris, France)
Le Guitarium (Paris, France)
Guitar Point (Maintal, Germany)
Guitar Select (Lyon, France)
Hendrix Guitars (Lavagna, Italy) (Truly ungodly prices)
Kitarapaja (Helsinki, Finland)
Paul's Bass Matters (Nijmegen, Netherlands)
Scolopendra (Bologna, Italy)
Tip Top (Stockholm, Sweden)
Vintage Guitar (Oldenburg, Germany)
Vintage Guitars (Rennes, France)
Woodstock Guitars (Aarhus and Copenhagen, Denmark)