I bought some 20mm (3/4") heat shrink, the cap will just go through with a bit of wriggling. I tested a piece before putting it on the lead and it will only shrink down to 10mm (3/8"). The lead is 1/4" diameter.
I'm back at work now and the sparkies have some 22mm (7/8") heat shrink with glue on the inside. I tested a piece and this will shrink down to 1/4" and the glue will help hold the braid in place.
I will put this on next week when i get home from work. Should do the trick nicely.