True to form, I've gone and done another 180 and have reverted back to using the dodgy Logitech MX Revolution. The cheapo corded mouse I mentioned that was "perfect" started moving my cursor around in a random manner; so I just had to get the MX mouse working again.
And, for the moment, it is working. Maybe there was a micron of dust inside the switch causing all the trouble - who knows.
To be on the safe side I've ordered what looks like an decent mouse, a Logitech M500 - main thing is that it's corded, so will be light and means I won't forget to charge it.
After it arrives, I'll post my opinion on it.
Oh, another thing, it's a refurbished mouse, so only £20 (about $30). Can't really grumble at that.