Pre-war BSA M24 Spare Parts
As we are dealing with bikes that are 80+ years old, New old Stock spares are in very short supply, and anything available tends to be expensive. 
M24 specific items in good condition, such as Cylinder heads & Barrels trade for £1000+, and some cycle parts such as rear stands and fork yokes can sell for up to £200+.
Many cycle parts were common to other 1937-40 pre-war M-series models, including the war time WD M20, and one or two specialist dealers may still have limited stocks of new WD parts.
Copies of the original parts books for 1938 & 39 BSA models are an invaluable asset when looking for spare parts. Reprints are still available from the National Motorcycle Museum bookshop as well as copies of other useful BSA literature such as Instruction booklets for individual models. These will provide illustrations of all parts with original part numbers.      It is useful to have a copy of BSA Service Sheet 703, Workshop data all models. This can be downloaded off the internet.

Factory Drawing of 1937 Pre-production M24 engine
Suppliers in Battersea, SW London provide a useful downloadable catalogue and price list for the WD M20 and keep a good stock of suitable, and often new old stock parts.

C and D,  tel:01564  795000.  long established BSA spares specialists, who can often assist with 1950's M and B series spares which are common to pre war bikes. 

Cornucopia.  Tel:05535 911114.. Excellent for BSA and hard to find parts. Tel:07742 611811.  Stainless steel Luggage racks, no drilling or welding required. Tel: +44 (0) 1454 260 596  for Motorcycle transfers. Tel:01379 586728. Barleycorn specialise in stainless steel parts, nuts and bolts, for BSA and Gold Stars.

John Harding: 01989750731, M:07973 889401, email:  Good for wisdom, pistons and pre-war BSA spares. 

F.W. Thornton. Motor factors, Pistons, Bearings etc. Tel 01952 252892

I keep a limited stock of parts and may be able to help. See For Sale & Wanted page  

M24 Petrol tanks made in India - BEWARE - These may look good from the photos, but they can have brackets in the wrong position, and the mounting holes for kneegrips & badges may   
also be wrongly spaced.  They may be cheap, but you get what you pay for and alteration(s) may be required.                                                                                                                                       

BSA Parts books