I have modified neiman steering locks (that the Mk3 was fitted with) to fit the Mk3 steel barrel. You have to get the barrel out to change the lock anyway. Neiman steering locks off ebay can be had for £11 Beware, you will need the key with the correct shape that allows you to access the lock when it is in the yoke. the ones with the square style key won't reach.
The hardest job is getting the little roll pin out that holds the barrel to the yoke, best way is to grind it out, or at least thin the wall with a tiny diamond burr.
Neiman steering locks are fitted to millions of bikes. Its the end that goes into the frame that has to be the right size and the right style of key.
PM me if you want to know more