I have been replaying Oblivion from an earlier save made last year.

After a variable period of play - 10 mins up to under an hour - the blue loading circle appears on the screen and runs constantly from then on.

Obviously this is ruining my experience of a great game, particularily when creeping through a dark dongeon when the blue circle is very annoying, drawing my attention away from the mouse pointer.

I have reinstalled the game but the problem persists. So I gave up.

I then started a new game in Morrowind and the same thing appears - the blue circle of death!

I then loaded up several saves of other titles in the GoG folder, they seem to be working OK.

This appears to only relate to the Elder Scrolls series, or is this a Windows fault?

Help would be appreciated.

I'e been playing 60 plus hours of oblivion on 2 different windows 10 machines. I've not seen this behavior. I wish I could give more information but it looks like it is the setup for your machine. Most of the time windows 10 should not interrupt a game if setup correctly.

Sounds like you can continue playing, with the blue circle added to what you would see normally? Does the blue circle disappear (temporarily) when you load a new game, and does it disappear when you quit the game? Does it happen reproduceably when you play Morrowind and Oblivion, after a few minutes, and it doesn't matter if you play a new or a saved game?
I can't offer you an explanation, not to mention a solution, just a few ideas / speculations:
Could be a hardware problem (I don't know if corrupted drivers might also cause something like this)? Potentially an incompatibility with something else running in parallel? You might try changing graphics settings, for example (minimal graphics, switch off everything which makes the games look better), or with compatibility settings (including reducing colours, resolution and switching off optimisations).
Good luck - it's highly unlikely that the games themselves cause this problem!