Suppliers

In no particular order except for the broad categories, a list of places that sell stuff that is relevant to our interests. Personal experience of these, good or bad, would be useful on the discussion page.

London services & workshops

Blueprint model shop They have a laser cutter, and may also do plastic board.
Hamar acrylic (ask for Terry). "Hamar tend to turn things around in a couple of days. They can do all sorts of complex plastic fabbing as well as simple cutting. Excellent variety of materials in stock."
4D Model Shop "They have a proper shop with racks of sheet material. They also sell the tools and laser cutting services. A quicker way of getting sheet material, but you'll probably have to cut it yourself."

Others to try:

London retail or trade counter

RS has most things, more professional. 4 london trade counters
Cricklewood Electronics A real shop, with little drawers of stuff & everything.
Maplin chain, more hobbyist. Getting really poor at actual components.
Cool Components Sparkfun stuff. Personal callers now allowed by appointment.
Kris Wines Wine and a great selection of beer.

London-based, primarily mail order

(not known whether personal calling is allowed)

Earthshine Arduinos and other parts (can sometimes be found on hackspace IRC)
skpang S K Pang - Sparkfun products and other parts

Mail order

Farnell has everything, more professional. Owns CPC and Newark.
RS has most things, more professional.
tinker.it
Amazon (next-day with Russ's Amazon Prime account) - equipment is often cheaper
Bits Box
Barend Hendriksen Holland. Interesting RF parts.
Keytronics Obsolete IC supplier mail order, can also be found with small parts at radio rallies.
Metals4u Metal stock, Aluminium, Steel etc. - Welding equipment.
Beers of Europe, King's Lynn A truly amazing selection of beer

Classified ads and junk sales

engineering machinery , materials and small ads
amateur radio rallies have lots of interesting junk and random components

eBay

I have dealt with these on ebay and received from good to outstanding service from them

the solderman soldering equipment (artag)
acuflow syringes (artag)
crodnet components (artag)
Spiratronics components (artag)

I have dealt with these sellers in the real world (and sometimes also on ebay) and will gladly use them [again].

pyedpyeman surplus radio gear (artag)
fazerblazer machinery and manuals (artag)
nezretroussez components and military radios (artag)
pcefficient ex-corporate IT equipment (artag)

These sellers seem to have particularly interesting and relevant products, but I haven't dealt with them yet.

vinyl cutting blades (artag)
John Stevenson from rec.models.engineering (artag)
gas-filled tubes (artag)