Hi Darren,
Further to Ed's advice, if your A32 is completely assembled save for the Clutch, and you have the buff log book there should be no problem in recovering the number, for this the bike has to be seen to be a complete original machine that is capable of being prepared for registration. When the new registration is received the bike will be classified as not licensed and as soon as you complete the bike, mot and insure it you can register it at your local main post office.
Should you wish to go ahead with an application for the bike email Len Boydell, the Douglas Club registrar and he will supply the forms that you need together with the information required by the DVLA. Basically he will need a photo of each side of the bike (plus, although not actually required but a bit of overkill does not hurt, a threequarte rear view with the number plate visible!) Also required is a photo of the frame number and engine number, alternatively a "brass" rubbing of both numbers will often be clearer.
A word of advice DO NOT post the buff log book to Len or the DVLA, if it goes astray its lost forever! Take it to your nearest DVLA office and get them to make you an authenticated copy, similarly if you have any mot certificates or tax disc relating to the bike.
Len's email address is douglasregistrar@talktalk.net
I have mentioned you to Len and he is happy to assist.
Regarding the other bits, unless you can obtain a frame with a matching buff log book you would need to apply for an age related number, to do this the bike has to be complete and running with an MOT and insurance.
You mention you live in outer London, if north of the river why not come along to a Douglas Club night we hold them in Chingford during the winter months, you would be very welcome even if you are not still a Douglas Club member.
Dave