The BMMC/MSA stuff & the MSVR stuff are two different entities, for want of a better word.
To get the Registration Card you need to fill in your details on the registration form & return it to BMMC; they will forward it to the MSA, who will send you a Registration Card (commonly called a licence) which will have your MSA number on it. The Registration Card & the Personal Record Card should be kept together.
The MSVR form is used to volunteer for their meetings - depending which circuit you're marshalling at you'll probably need to get volunteering forms from every club you want to marshal for, although at some circuits, e.g. Oulton & Anglesey, you can do everything on one form...or you can use:
http://www.marshals.org.uk/
Your first priority should be to get yourself down for a training day. You can find out about & apply for these, along with other useful stuff, at:
http://www.volunteersinmotorsport.co.uk/
If you haven't already got them, it would also be worth downloading the Pocket Guide to Marshalling & grading manual from the BMMC website.