Just heard from Nervous Nelly after her trip to see this Volvo specialist. After reading the fault codes (sorry - don't know what he was using) he has confidently declared the problem to be....
The accelerator pedal; which I take to mean the throttle pedal potentiometer.
The guy said he'll go away and come back with a price for the part and advised not to drive the car on any long journeys until it is fixed.
I've enough experience to know that changing the part won't
necessarily fix the problem but it's probably worth a shot. When I did the same job on my Range Rover the part was about £100 and took 10 minutes.
For anyone based in West London note that this Volvo chap works out of the same premises as 'The Jag Workshop' in Ealing that looks to be a very interesting place as their website shows:
http://thejagworkshop.co.uk/
loads of E-types and other classic Jaguars. It was friend with an XJS who recommended giving them a call.