The cheapest fix is the plastic bags you get from the grocery store. I always keep a few in my Mini for just that reason or when going to the car wash. Cover the distributor with the bag if it looks like rain or pull over somewhere (gas station) pull a bag and cover distributor and keep going. When it stops raining, take it off. That easy.

I use spray silicone on the cap and wires.  I clean and add a couple of new coats once a year or so.  It seems to work very well.

Get a new dizzy cap , then try to find a dizzy cover from a mini clubman to protect it from the rain . In the old days we use to use things like ice cream containers, rubber gloves, a peice of plastic attached to the grill just in front of the dizzy and a few other things that I have forgotten, come on guys lets know how you protected your distributor from wet weather.

Robin, the coils will work wired either way but they produe more energy when wired "correctly".  If you have damp weather losses and a reversed coil there is indeed a chance that you will loose enough spark energy to stall.

There are lots of ways to keep the dizzy dry.  I use a simple piece of sheet rubber attached to the back of the slam panel that hangs like a skirt in front of the dizzy.  I don't drive much in the rain either but those times I have... my car has not had any problems.

There happens to be a discussion on the www.mokesinc.org forum:

In one of the replies, "I used to have an old Mini which I converted from positive earth to negative earth, by reversing the battery and flashing the generator. I didn't realise that you needed to swap the polarity of the coil. It ran OK, but as soon as the weather got damp it would start to misfire then I'd roll to a stop...."
Could this be a contributing cause to the original poster's problem? His profile doesn't show what vintage his Mini is so no way of knowing if it might have been negative ground at one time...

Edited to add a link to said discussion:
//www.mokesinc.org/index.php/topic,8640.0.html

Sometimes it is just dirt on compromised (worn out) ignition components.

When you have tired spark plug wires they develop micro cracks that allow the spark to leak out. In the dark (really dark) you can see the spark travel along the outside of the wires, jumping here and there and not getting to the plugs. (Kinda neat light show!) Dirt, even a tiny amount of grease as from touching the wires wiht greasy hands) acts as a conductor to lead tha spark charge to ground. The oil/grease gets burnt to carbon and carbon is a good conductor. Dirt also helps hold moisture, so you get wet weather problems.

A worn or dirty distributor cap also drains away spark. You have to keep the outside clean (clean as a CD or DVD for example). But it can also fail inside - as it gets dirty inside (an invisible film) the dirt can conduct spark away. The route the spark travels ends up as a carbon track that saps away the zap.

If you keep things clean and fresh, you don't need rubber gloves, WD40 etc. Spraying lots of WD40 around to displace the water (thats what "WD" stands for - water displacing) leaves a film that... guess what.... attracts and holds dirt, which holds water.

Of course keeping it properly tuned with good points and condenser and proper timing and dwell means you get the best spark at the right time.

thanks for tip. Is the minimania one generic to fit a 74 witha 1275 ? thanks again

I've never had the problem.... Don't get out in the rain if I can avoid it because, in a topless/side curtain-less Moke, yer gonna get wet.  I have been caught out in some real gully-washers though and the car never skipped a beat.
Perhaps some of the ignition components are compromised. I would through a new cap and a decent set of wires and see if the problem goes away.
If not, I've heard of a couple of things to keep you going.
1.) Punching some holes in a surgeon's glove, cover up the distributor cap.
2.) WD40 can be your friend.
But, the whole thing should work without resorting to those measures.....

There is a splash shield that was mounted to the slam panel, in front of the distributor, to stop rain and splash coming in from the front.
There was also a cover, of sorts, that would slip over the cap and fit tightly over the wires....can't find that though

see diagram

//www.somerfordmini.co.uk/eshop/index.php?main_page=page&id=75

 oops
There's this thing as well
//www.minimania.com/web/item/NJT10004/InvDetail.cfm

When it rains the moisture is coming through grill and from pavement and stalls or kills engine . I have to wait for it to dry out to restart. Of course distrbutor and related electricals are directly behind the grill . Any fixes or solutions ??