Ten Foot Tall
661 EOF = mid-61, Birmingham (so BSA?!?!) could be a 1961 BSA A10 or A10 Super Rocket indeed
Registration number: 464 ABK ✓ Taxed Tax due: 01 June 2017 ✓ MOT Expires: 14 June 2017 Vehicle make BSA Date of first registration May 1962 Year of manufacture 1962 Cylinder capacity (cc) 650 cc Fuel type PETROL Export marker No Vehicle status Tax not due Vehicle colour BLACK The others are HMY 34B = 1964 (nothing found), VXM 826 (Aug 58 - July 59 "allocated in blocks", nothing found) and 661 EOF. Probably not an RGS given that it is now black? Best guess is A10 or A10 Super Rocket.
I think it is a Rocket Gold Star ( RGS ), Reasons- Falls right in the middle of the short production run 61-63. They are Black and Chrome ,is chrome a colour? It survives , people hung onto Gold Stars of all types.