Aircraft, other than those mentioned under paragraph 2.4.3 or Appendix A, are all required to have an AFM.
Here is para 2.4.3 for the snooker table!
The following aircraft may not be required to have an AFM:
a. aircraft up to a MTOW of2,722 kg (6,000 lb) manufactured and flown prior to 1 March 1979
b. historic and ex-military aircraft
c. amateur-built aircraft
d. experimental aircraft
e. hang gliders operated under Civil Aviation Order (CAO) 95.8
f. ultralight aircraft operated under CAO 95.10 and CAO 95.55
g. gyroplanes operated under CAO 95.12 and CAO 95.12.1
h. weight shift controlled aeroplanes and powered parachutes operated under CAO 95.32.