We are travelling to Cornwall from the east mids on the first Saturday of the summer holidays what's the best time to set off to avoid traffic? We can't check in till 4pm so didn't want to have a lot of time with no base to go to as we have 3 young children.

Honestly, you're going to be stuffed whatever time yo leave.
Just allow a couple of hours extra and make many stops on the way.
Take it slow and steady and make an event of the travel.