I'm a bit confused - as far as I'm aware leafspring COB Cobras were all fitted with Lucas dynamos, not alternators. As you say, COB6029 has a dynamo. So for a UK car I don't think there is a correct alternator. Are you planning on going down the CSX route?
COB6029 has a Lucas C40 dynamo with smooth casing, not stepped as in some applications, There is a tachometer drive from the rear casing. The gearbox for this is sold for Frogeye Sprites, from such places as AH Spares in the UK. Cables are also reproduced. This dynamo had a fabricated support bracket, which is now reproduced by Hawk Cars.
The fun comes, as Dan notes for alternators, with the pulley and fan casting. A single aluminium casting can be found from (e.g.) a Sunbeam Alpine (15mm shaft), but whilst the fan is the correct size, the pulley is smaller diameter. This will charge a little better, but will affect the tachometer accuracy. Your tacho may need recalibrating to suit. I have never seen an original Cobra large-diameter pulley for sale, and it was not used on anything else that I know of (even Sunbeam Tiger, which used the Alpine size I believe).