No, and yes, respectively.

BS1363 dates from 1947.
All rewireable BS1363 plugs have a metal earth pin.
Class 0 table lamps were banned from sale in about 1975.
Class I (earthed) and class II (double insulated) are permitted.
Only moulded plugs for class II equipment may be made with an ISOD (
Insulated Shutter Operating Device) which is a plastic earth pin.

Martin.

Peter Easthope wrote:
Hi,

Does installation of a BS 1363 plug, with a ground pin, on a two
conductor cord of a table lamp, violate wiring regulations? I don't
imagine an unconnected ground pin posing a hazard.

Does a lamp in Britain ever have a cord with a ground conductor?

Thanks, ... Peter E.