We would like to go to Devon and Cornwall, but without a car. Where could we base ourselves and does anyone know of any day trips or or preferably multi-day trips that we can access in early or mid June without going from London?
As you probably already know, Devon and Cornwall are not very conveniently served by public transportation, but that doesn't mean it's impossible.
The following web pages may be useful.
https://www.visitcornwall.com/travel-to-cornwall-train
https://www.visitdevon.co.uk/visitor-information/getting-around-devon
Tell us more about what interests you and how many days you have.
Thanks, We like history, great views and quant towns with good pub food.
So, the combination of public transportation and quaint towns is fairly rare, because bus (and more so train) routes have to cater to major population centers and work schedules. That said, you can get to St. Michael's Mount by combination of train (to Penzance) and bus (to Marazion). IMO "the mount" is one of the most magical places in all of England.
https://www.stmichaelsmount.co.uk/getting-here/finding-us
https://www.stmichaelsmount.co.uk/
While in Penzance, you may enjoy some of the things listed here https://www.visitcornwall.com/places/penzance
It is also a short (less than 1/2 hour) train ride to St. Ives. See also https://www.visitcornwall.com/things-to-do/attractions/north-coast/newquay/cornwall%E2%80%99s-great-scenic-railways
I don't know as much about Devon. Hope the above gives you some ideas. If you're going this year in early or mid-June, many accommodations may be already booked, so the sooner you decide where you want to sleep, the better.