Ah! The 2 engine variant of the A340 Bearing in mind the size issue, might it have been one of the very new private B787's ? You never know, it meets most of the noise and environmental demands of the day.
I sent him a link to a photo of a BBJ and his first comment was "No turny up wingy things on the one I saw". Many BBJ without winglets?
While that description does fit the 787 I though the restrictions at Farnborough were based on a maximum empty weight of 80 tonnes, and a quick look at Wikipedia suggests a 787 tips the scales at 118 tonnes.
787s are above the max MTWA of 80 m/tonnes.
MTWA? Maximum Takeoff Weight Authorized?
Waiting to hear back from him what time this was, but a BBJ or ACJ still seems like the most likely scenario.