You don’t say if your Brum has a Miller or a Lucas distributor (DKX2A). The Lucas one is easy enough to find points for as the same basic distributor was fitted to a number of other bikes in its twin cylinder variant, including the Sunbeam S7 and S8, Royal Enfield 500cc twins, etc., whilst the four cylinder variant was fitted to Ariel Square Fours, and many thousands of small British cars such as the Ford Model Y Tudor, late Austin Sevens, Morris Eights, etc..
If however you have a Miller distributor, things get much more difficult… The only Miller specialist I can think of who may be able to help is Malcolm Leech ( Leach ? ), who advertises regularly in the classic press, especially “Old Bike Mart”.
Both types are prone to rapid wear as they spin at engine speed instead of the half engine speed that they operate at on a four-stroke engine, so do check for wear generally, starting by trying to rock the shaft to check for sideways play. If there is any discernible play timing will be out as the points can open and shut just about anywhere they fancy ! Replacement bushes are available for Lucas distributors, and some folk have converted them to ball bearings, which are much better.
Good Luck !
PS You could also try a distributor rebuild specialist such as “The Distributor Doctor”, who advertises in classic car magazines.
I should have said, it is a Miller distributor.
I shall carry on looking for something to adapt.
It’s a bit more difficult finding old parts over here in France, for some odd reason nearly everything appears to be in metric dimensions.
In addition to Brian’s sound advice, I would suggest that you look at the catalogue of a UK supplier of ignition parts, “Independent Ignition Supplies”, https://www.magneto.co.uk
Among other things, they specialize in platinum points (quite expensive), which can replace the original tungsten(?) points in the Miller distributor. The original contact breakers must be used, but new points can be screwed or riveted on.
I have never dealt with the firm, but their catalogue looks interesting.