In Original Austin Healey Clausager says on page 47 referring to the plate David inquires about: "Early 1953-1954 BN1 models have this plate giving car and engine numbers on the scuttle side casing just in front of the door." and also that "In addition, these early 1953-1954 BN1s also have a chassis plate on the right-hand chassis rail by the master cylinder bracket."
And, as Simon says, after Austin went to unified numbering the plates became as shown in his post--a long oval--located along the left side of the footwell (or at least this is how it is in my late 1954 car #222333 which is also left-hand drive).
Anderson/Moment say on page 50 that on most later cars these later plates were mounted to the firewall in the engine compartment but on some cars were mounted in the interior footwell--so I guess for later cars either location is correct and where the plate was installed depended upon who was doing the work and how his back felt that day!