Every year I have problems starting the Red mini when its cold and damp. Its had new plugs and leads, condenser, points, rotor arm and cap. But today it's cold AND damp and just wont start.

I was looking at this:
electronic ignition

What do you think?

The electronic ignition may help as you've already replaced most of the other ignition components. However, do make sure your choke is properly adjusted and that your ignition timing is right before you invest any more money.

The conversion typically mentioned first is the Aldon Ignitor. Over the past year there have been multiple discussions on The Mini Forum about the "Britparts Kit" primarily aimed at Land Rovers with the 45D4 distributor. I believe this would fit your car as well but you may wish to post this question on TMF to see what others say. I believe the BritParts kit is even less expensive than the one you posted the link to and I have yet to hear anything bad about it.