British/Swiss Honeymoon later this year….best time and places?

Looking to go to Europe for the first time basically and ideally seeing some of the UK and also some of Switzerland (or northern Italy).

Switzerland in particular because we want to see some of the mountains and stuff there while also having nice towns/cities nearby with European architecture and similar with Northern Italy which is close to Switzerland. Not sure exactly which cities to visit though in those countries.

Around 7-10 days would be our ideal. Not that interested in doing anything in particular outside of just walking/sightseeing and maybe taking in a football match.

We're traveling from North America, I personally hate the heat and also want to avoid the busier tourist season so was thinking September, possibly October if it's still warm enough to walk around in.