Must be where the Hidcote variety of lavender comes from!
To add to the Ireland discussion – my favorite town on our too-short trip was Westport. Driving the Wild Atlantic Way through Connemara and up the coast from Galway was spectacular. And Westport has great outdoor activites (bike rentals, kayaks, beach, etc.), good restaurants (best on our trip) and great bars.
A side trip from London that I remember best was Hampton Court, walking up the stone steps from the kitchens, so worn in the center, I could really feel the age and history there.
Regarding Scotland, I’ve been twice and want to go back. We actually loved Glasgow even more than Edinburgh- the University is gorgeous (see the cloisters) as well as Kelvingrove Museum (see the Dali); The cathedral, the Necropolis, the west end, we loved it and will go back. I loved St Andrews, too, just loved walking around the town, the sands, the boats. Highlands were fantastic, I want to return to Skye & also back to Loch Ness. Dores Inn on Loch Ness near the Inverness side had the best fish & chips we had on our trip 
I’d like to take the North Coast 500 road trip.
All three countries in one trip means a bit more skimming the surface, rather than in depth, not a problem, it will show you the places that speak to you & you can go back for a follow up visit to your favorite place.
In Scotland last month we took the ferry from Isle Skye over to Isle of Raasay and stayed at Raasay House. The Cullen Skink was the most delicious soup I have ever eaten!