The restoration, even at huge cost, of what English Heritage calls one of “the great lost gardens of London” sounds a worthwhile, even noble, project. But what if that “lost garden” is a myth, a pipe dream never really built? English Heritage plans to transform the estate of Marble Hill, a grand house by the Thames, by reintroducing elaborate gardens it says were inspired by Alexander Pope, the satirist and poet, and 18th-century royal garden designer Charles Bridgeman.

The original designs featured a ninepin bowling alley, an ice-house seat and a flower garden, surrounded by twisting paths and groves of trees and English Heritage plans to recreate all this, alongside a “vibrant” cafe and children’s play area.

Yet the Marble Hill Revived scheme is based on flimsy evidence, say campaigners, who have carried out their own detective work and suspect that history is being subverted to modern ends. “How can English Heritage make the assumption that, because Bridgeman visited the park on a single occasion, he not only advocated the landscape scheme but also laid it out?”, said park campaigner Janine Fotiadis-Negrepontis, who hopes to stop the radical redesign.

Her fellow Love Marble Hill campaigners believe that the two famous men had little to do with the gardens which were actually built – and now enjoyed by thousands of visitors each year – and that English Heritage has secured a grant of £4.1m of Heritage Lottery funding on the basis of disputed historical connections. They suspect the charity, which runs 400 historic sites across the country, aims to create a viable events venue on the site, with a large cafe and manicured gardens, simply to ensure an income stream for the future.

A painting of Alexander Pope by Irish portrait artist Charles Jervas. Photograph: Getty Images

“In order to unlock large amounts of funding, English Heritage has to show the important history of our park and how unique it is, and this is the reason why references are made to Pope and Bridgeman in the Lottery funding application,” said Fotiadis-Negrepontis. “English Heritage itself has discredited Pope’s 1724 plan and there is no evidence the later plan was really laid out; archaeological works undertaken by Historic England found nothing to support that. It really is a case of the emperor’s new clothes.”

The campaigners have already had some success. An earlier English Heritage planning application put before Richmond Borough Council was withdrawn last year when a petition in opposition attracted 4,000 signatures. The charity now seeks to submit revised plans this summer.

Bridgeman was the leading name in landscaping in the 18th century and has been described as “the last great gardener to work thoroughly in the French tradition”. Pope, the author of satirical essays and poetry such as The Rape of the Lock, also had a strong interest in garden design and lived in a neighbouring villa.

Speaking this weekend, Anna Eavis, curatorial director of English Heritage, denied the basis of the campaign group’s key objections and said that after extensive research the charity stands by the links to Pope and Bridgeman. “We have found archaeological indications, bills for payment and engravings, and we have worked with many different expert bodies on this, including the Environment Trust. Yet at the same time this is about interpretation, and so we are holding a symposium in June to present the case. If there is new evidence, we will consider it. We have no plans to run large corporate events on the site.”

Marble Hill House was originally built for George II’s mistress, Henrietta Howard, who became the 9th Countess of Suffolk, and the campaign group queries whether she could have had enough money to carry through such an expensive design. “It was well known that Henrietta’s purse was depleted with ongoing building works at Marble Hill at this time,” said Fotiadis-Negrepontis, adding that Pope’s fellow satirist Jonathan Swift poked fun at her lack of funds in 1727 when he wrote the lines: “My house was only built for show, My lady’s empty pockets know; And now she will not have a shilling, To raise the stairs, or build the ceiling. Tis come to what I always thought, My dame is hardly worth a groat.”.

The Love Marble Hill group also points out that contemporary paintings, including works by Augustin Heckel and Richard Wilson, do not show signs of the Bridgeman plan.And the only reference it can find to a bowling green is in a bill for a paint called “bolling green” used on railings in the grounds.

English Heritage argues that proof of the grounds’ more complex layout lies in a sketch drawn on a document found in Howard’s archives at the Norfolk Records Office in 1991. The campaigners, on the other hand, argue this is really a prospective blueprint and not a factual survey of what was already there. The garden historian David Jacques, whose book Gardens of Court and Country came out last year, told the Observer he believes the campaign group is guilty of wishful thinking. “If you don’t like something, you just refuse to believe it and I think this is what is happening here,” he said. Jacques worked as a consultant for English Heritage 10 years ago, but said he has no current ties to the charity. He remains convinced of the link to Pope, persuaded partly by doodles on the manuscripts of some his poems which look like ideas for Marble Hill.

Some of the opposition to the English Heritage scheme is fuelled by fears that a large amount of woodland will be sacrificed. The local Site of Scientific Interest, Love Marble Hill says, is a home for song-thrushes, bats, owls and badgers.

The charity, in turn, states that Marble Hill’s tree stock is in decline and that only shrubbery and diseased trees will be targeted. It also plans to open up the house to the public for more of the year. The English Heritage website makes a financial case too: “In 2016-17, it cost English Heritage more than £200,000 to run Marble Hill. As a charity, we cannot sustain that level of cost and the Marble Hill Revived project will help to reduce the overall running costs.”

The park has been a political battleground at least twice before. At the beginning of the 20th century the Twickenham community fought off a plan by the Cunard business to build a housing development. Its defeat led to the Open Spaces Act of 1906.

Then in 1986 the park was controversially handed to English Heritage when the Greater London Council was abolished by Margaret Thatcher.