I can also thoroughly recommend Johns covers
There are covers that just go over the cockpit but if parked up in torrential rain, I think its best to have one that covers the bonnet as well for the sake of a bit more material
Johns are very easy and quick to fit with elastic over the lamp housings and elastic over door handles etc
one of the best accessories I have ever bought for the Morgan - never travel anywhere without it stowed away in the back and have needed it on quite a few occasions
another top tip - also have a large thin tea towel or similar towel with you as well in a waterproof stuff stuff sack to wipe away any pooled water on covers and hoods before you either take off the cover or roll down your hood after heavy rain