The former model - who opened VBites in Brighton, South England last year after receiving a £24.3 million divorce settlement from ex-husband Sir Paul McCartney - has shut the doors on the eatery, for a supposed "summer break", but insiders insist the business is in trouble and is unlikely to reopen.
A cafe insider said: "I understand Heather has been haemorrhaging money on VBites for a while now. A six month `holiday` isn`t usual."
Locals have claimed the business was deserted during the busy summer season while Maura Hughes, who lives nearby revealed she heard about the closure from the restaurant`s head chef.
She said: "He`s not happy about it at all."
Other residents have insisted the venture won`t be missed if it shuts down for good.
Truck driver Tom Brown said: "I`ve never used it and I never would apart from maybe using the loo. I`m not a vegan, it doesn`t really interest me and I heard the food was rotten.
"I`ll be glad if it changes hand so I can have a proper cup of tea or coffee with real milk instead of the stuff they serve there."
However 42-year-old Heather - who has a six-year-old daughter Beatrice with the Beatles legend - has angrily denied the restaurant is to close.
She tweeted: "VBites had a great summer, the success has brought us many opportunities to become worldwide.
"We are so excited to start our franchise projects and spread the Vegan ethics, training classes, cookery classes now our cafe is in its wintery weather season. Keep updated on VBites.com and thanks for all your continued support. Hx (sic)"
A statement on the restaurant`s website said: "We have had a fantastic summer and - like many beach cafes across the country - will be closed over the winter so that we can focus on staff training, recipe development and VBites franchising."
An answering machine message for the restaurant said the venue would reopen in spring, but failed to give an exact date.