I have done a number of back to back Rick Steves tours, including the South England tour combined with the Best of Scotland. We did a week in London ahead of time and a few days in Scotland afterward. We went mid-May, so finished the Scotland tour by mid-June. Weather was generally nice but we had drenching rain a few days in Scotland (the Iona day). No midges though!
I had also done the Best of England tour several years before with a back to back of Paris and Heart of France.
TBH, by the time we got to Stirling Castle at the end of the Scotland tour I could not summon the energy to visit one. more. castle. I was totally shocked at myself but there were just too many castles/ruins/same kind of thing on these 2 trips. I generally thrive on them but by this time everything had a sameness about it by the end.
My new rule after that is to choose 2 different cultures for back to backs. TBH, from London where the Best of England ends it's actually quicker and easier (pre-pandemic) to get to Paris than to get to Glasgow where the Best of Scotland now begins. If you are going for 2023 then the Eurostar from London to Paris may be back to being easy again. Only 2+hours city center to city center. Of course, have no idea if you are interested in France or not!
Editing to add: I went back and re-read my Trip Reports for 2015 (Best of England/Paris and HOF as well as Best of South England and Best of Scotland). I forgot several tour members had discussed back to backs on the Best of England tour. Another couple was doing Best of Ireland and Best of England and indicated they felt a sameness to it while one couple had done Portugal and Best of England and was having a wonderful experience with 2 different cultures. Up to you of course as everyone needs to make themselves happy!