Well, it obviously is a BJ7. The L is for left hand drive.
The 20327 is the chasis number indicating it was built in 1962, Those built in 62 ran from 17551-21782. So I would guess it was built around Sept-Oct-Nov., 62. You can order a Heritage Certificate which will the engine number, original colour,date of build and despatch, as well as factory fitted equipment. Cost use to be $50, but I think it is a little higher now. Adress: BMIHT Registered Office, Banbury Road, Gaydon, Warwick CV350BJ or see if British Motor Industry Heritage Trust has a web site.