Are you sure that the '4' refers to 'damped'? I've had several of these over the years on various cars, and just like the one currently on my Cobra, the needles have never appeared to be damped. It usually oscillates so quickly it's quite hard to see, and there's no damping mechanism visible inside.
I didn't bother too much about the actual part number as it's not visible when the instrument is installed. They do come up on ebay UK now and then, but you have to plough through a lot of motorcycle versions to find them. Nothing showing at the moment, though - I'd search 'Lucas ammeter' or 'Lucas amp' on the UK site. 'Lucas amp' throws up this, which is only a 20-0-20 but could easily be refaced:
VINTAGE JOSEPH LUCAS BM4 20 AMP AMMETER GAUGE FITS AUSTIN MORRIS RILEY MG | eBay
Roger