I am new to the forum and indeed Morgan ownership and know that many experienced Morgan owners will have their preferred bags and cases for touring. Having said that I have quite by chance found a bag that really does seem ideal in that it is good value, waterproof and comes in a variey of sizes that fit Morgan racks well. Available in red and black with plenty of places to attach retention straps.
It is the Highlander Lomond Tarpaulin Bag. What makes it interesting is that it comes in three sizes and it is slightly "sausage shape" - in other words it uses the width of the rack but keeps the height profile low and therefore rear view visibility is not impeded at all.
The 120 litre bag slightly protrudes over the edges of my standard width rack on each side but as I have a relatively "high mounted" rack that is not a problem at all - about three centimetres on each side. But if you have a low mounted rack and are worried about blocking brake lights and want to be extra cautious the 90 litre bag is perfect. If you go on the Big Orange Watersports website they gave me good service and it gives the exact dimensions but plenty of places sell them.
The 120 litre bag is really very large and I cannot imagine filling it even on a long tour.
I can do photos of the 120 litre bag, 90 litre and 65 litre bags sitting on both a low and high mounted rear rack if anyone needs it though have yet to post a photo on here.
As I say I am sure there will have been many recommendations in the past and I am not trying to be a subject matter expert but have been so impressed with the unique fit for a cheap price for a quality product I thought I should share it! I have no connection with the manufacturers or retailers.