Why the chuff is my chain slipping?

[KneesUp]

Perhaps it's time you invested in a new derailleur for your antique bike and renew everything else at the same time?

It's not a velocipede - it's a steel frame that is functionally identical to any steel bike you might buy now except it doesn't have the apparently mandatory disc brakes. I'm not a great beliver in replacing things that still work; I don't really see the point. As mentioned above your post, the bike now has a different (lightly used, perhaps 3 years old though) derailleur from the parts bin. Shifting is now back to normal.

Does it only happen in one gear or in different positions ? As you have changed the wheels and it still occurs then I would have thought that it points to the a fault with the rear derailleur ? Is the tension on the arm sufficient to take up the slack of the chain or is it loose and allowing the chain to jump ?

You are correct - it was across the full cassette on both wheels.