Doesn't need a private one.
Just the only people that really want to talk to you are the Area FISO's in Scottish or London.
Weekend when there isn't mil traffic around have a look at the amount of airspace where realistically the only person you can talk to is one of the information units.
Take a fictional transit from just south of Dalkieth remaining clear of NEW and routing down to the east of the A1 IFR (I follow roads) to say Turwesten
The only time anyone will start getting someone interested with you is when you get near Eastmids which has always been a quite a pro GA set of controllers. And actually I more than likely would speak to them.
The only thing you have is Scottish Info and then London Info.
I might have forgotten one of the RAF bases might be open for something but if it is it will be a basic service with nothing passed so you might as well not bother.
Thought I would add that in for educational purposes.
BTW that's a fancy one it has nav aids and a carbon monoxide detector.
Another example who is going to look after the airspace over fife when Leuchars radar gets cut. I really don't think Edi has enough capacity to give any meaningful service unless a plastic pig is going into Dundee.