The project for a visitor centre and new landscape near the stones was one of several schemes that were torpedoed by the Government last week to save around £11bn.
Landscape architect Chris Blandford, whose scheme for the site won planning approval last year and was due to start on site shortly, said he was "gutted".
"At this moment we can't comment under confidentiality rules and have had no formal instruction from English Heritage," he added.
"We had hoped to start onsite very soon. It was exactly the wrong moment to have it withdrawn. We are pretty gutted but, you never know, funding may come through."
English Heritage said it was "extremely disappointed" that the £10m promised by Gordon Brown last May had been withdrawn.
A representative said Stonehenge was a key feature in Britain's bid for the 2012 Olympic Games and transforming the setting was vital to Britain's reputation.