Here is a list of piano shops where a piano can be bought or hired (please keep in mind the conditions and prices often change):
Steinway Hall: Steinway, Boston and Essex pianos; best place to go if you can afford the prices; no hire.
Chappell of Bond Street / now Yamaha Music London: Yamaha, Kemble, Bösendorfer etc; main place for Yamaha pianos; no hire.
Blüthner: Blüthner, Irmler, Haessler, Rönisch etc; to buy, hire and hire with option to buy; brand new pianos for hire..
JReid Pianos: Barraud, Bechstein, Bell, Bernstein, Bluthner, Bosendorfer, Boston, Brinsmead, Broadwood, Carl Schiller, Challen, Challen, D’Este, Erard, Fazioli, Fenner, Feurich, Gaveau, Gebruder, Grotrian, Hoffman, Ibach, Kawai, Kemble, Knake, Knight, Lipp, Matz, Pleyel, Pleyel, Reid-Sohn, Ronisch (Rönisch), Sames, Samick, Sauter, Schiedmayer, Schimmel, Seiler, Squire, Steck, Steinmayer, Steinway (Steinway & Sons), Steinweg, Thurma, Weber, Welmar, Yamaha; to buy, hire and option to buy; new, second-hand and restored pianos; second-hand pianos for hire.
Morley Pianos & Harpsichord: Bechstein, Hoffmann, Grotrian-Steinweg, Bentley, Ritmuller, Weber, Monington & Weston, Waldstein and Steinbach; to buy and to hire, new and second-hand.
Piano Warehouse: in Willesden and Surbiton; to buy and to hire; many different brands, lots of Yamaha pianos.
Markson Pianos: to buy or to hire; many different makes; Bechstein piano centre in London
Mark Goodwin Pianos
Little & Lampert Pianos