Google shows various companies for hiring bikes in the UK. As these web pages change I'll leave it to you to do a fresh search when you need to rent a bike.
Also check MCN for hiring bikes in the UK.
Here is a list of the numbers as advertised 22/4/98
Adams - 020 8 980 0063
Easy Rider - 020 8 723 7223
Freeway - 01132 534423
Happy - 020 7 252 6392
J+C Bikes - 020 8 570 0326
Kent Hire - 01634 712589
Hire - 0831 535116
Riverside - 020 8 983 4896
Stavs - 020 7 538 2843
Worlds End - 020 8 746 3595
Fowlers (Bristol) - 0117 9770466
Fowlers (Cannock) - 01543 428528
TPC Hire (Fareham, Hants) - 01329 668994
Carnell (Doncaster) - 01302 327722
Carnell (Peterborough) - 01733 223444
Carnell (Nottingham) - 0115 939 1900
Carnell (Milton Keynes) - 01908 325700
Woods (Abergele) - 01745 822922
HGB (Ruislip Manor NW London) - 01895 676451
Phoenix (Corby) - 01536 264990
Raceway (West London) - 020 8 749 8181
Raceway (East London) - 020 7 237 6494
Metropolis (London) - 020 7 793 9313
West Pennine MC Hire (Blackburn, Lancs) - 01254 698907
Banjax (London) - 020 7 729 5228
London MC Hire (London) - 0800 0680 992
Alvins (Scotland) - 0131 555 1039
Note: To dial these numbers from outside the UK replace the initial 0 with 44 and precede with your country's international direct dial prefix.