Gaydon was the name of a proposed service area on the M40.
Mobil's plan was built on an idea initiated by the Department for Transport. Blue Boar were hoping that by coming up with their own idea at Gaydon, the Department would be forced to go for the cheaper option where most the administrative work had been done by Blue Boar for them. This didn't work, as the site at Warwick was seen as being better in most respects, not least because it didn't pass traffic through a low-capacity junction. Even so, it was one of a few clashes which eventually saw private companies given full responsibility to develop service area plans.
Fuel would have been provided by BP.
Long before the M40 was built, engineers intended to build services near Gaydon and Chesterton. They never got as far as recommending specific sites, but if the policies hadn't changed they would have gone on to investigate a service area near Gaydon.
In 1995, a report in The Guardian claimed that nine different developers were proposing services in the vicinity of M40 J11 and J12.