I second the advice about the rain shield. I saw them all over London-they look like a plastic cover that goes all over the stroller. Seems like the baby wouldn't like it, but I guess it beats the rain.
Now, you must prepare yourself for a trip with a child by having extremely low expectations. Almost all parents can tell horror stories of their first or second vacation post-baby. They may not sleep well, a newly crawling baby may refuse to stay put in a stroller or high chair, and just the exhaustion of parenting added to travel can really take its toll. Once, my youngest, who steadfastly refused to use the toilet at home, insisted she had to use every public toilet on a trip. She didn't actually use it, just pretended. You may be ready to collapse, but baby may need to be walked around just to go to sleep. I don't want to scare you too much (not possible) but just prepare you to take it really easy on yourself and back off your itinerary if needed. May the happy baby fairies smile on you.
One more thing-the Scots are much more willing to burst into song than Americans. Maybe you can get someone to sing lullabies to your bairn.