Chassis number 40 was left in the barn in 1974 and was there until discovered by Coys a few weeks ago.
It has never moved, although the engine was fired up some five years ago and turns over freely.
"This is a really amazing find which has got the Jaguar world really excited," said Chris Routledge, Managing Partner at Coys.
"The 1961 car is in amazing condition considering where it was left and interest is going off the scale."
He added: "But this is not the only Jaguar find; we are also selling an XK120 Roadster - reported to have a competition history - that was found in a lock-up in Essex.
"The last XK that we sold in this condition made over £90,000 and we expect the E-Type to do exceptionally well... E-Types have been increasingly sought after since the 50th anniversary of the marque, with collectors looking for early Series 1 chassis numbers."
Other cars featured in the Spirit of Motoring Auction, which takes place on October 26 at the Ascot racecourse on the outskirts of London, include a rare Connaught L3 racing car from the collection of Ian Hill of Judas Priest; one of the finest Jensen 'Interceptors'; a Vignale FF model that the auction house has never seen before and a fabulous example of early motoring, a Ford Model T Speedster.
Alongside another highly original car, a Bentley 3.5 Litre, Coys will also be offering a Bentley Eight, directly from the collection of television legend Bruce Forsyth.