Thanks for your advice, people!
I have taken it to Sportomotive in Bournemouth who had the correct piece of kit. He looked at the machine and found that the MAP sensor was giving incorrect readings at idle.
Cos had had a similar fault with another Elise recently and the problem with that was an issue with the wiring loom.
He has just phoned me and let me know that it was the same intermittent fault with mine that meant that my VVC valves were in the wrong position for idle, so when I was giving it some "beans" it was acting fine, but when I slowed down it was running really rich and lumpy. Apparently: fix the loom problem - fix the running problem! Brilliant!
Hopefully, I can pick it up tomorrow and see if that has fixed it all!
On the bright side I should not need any sensors changing for a long time now!