Plans for a major development on water meadows on the edge of Bath will ruin one of the city’s most historic and beloved landscapes and could put at risk its world heritage status, protesters claim.

The city’s Conservative-led cabinet will meet on Wednesday to discuss a new park and ride scheme and is expected to back one of two sites on Bathampton Meadows to the east of the city.

Campaigners plan to stage the biggest protest Bath has seen, claiming that a park and ride will ruin lovely views of the city including from Solsbury Hill – celebrated in the Peter Gabriel song – without solving the area’s traffic problems.

They have appealed to the UN’s heritage committee to intervene, pointing out that Bath’s “garden city feel” is an important factor in it being given world heritage status.

One of the leading campaigners, Christine Boyd, said: “The tragedy is they will ruin one of Bath’s most significant and historic landscapes while hardly making a dent in congestion and pollution.”

About 13,000 people from Bath and the surrounding villages and visitors have signed a petition calling on Bath and North East Somerset (Banes) council to ditch the plan.

Susanne Hagen, the chair of highways on Batheaston parish council, one of three villages that overlook Bathampton Meadows, said people were outraged that millions were being spent on such a scheme at a time when services were being cut.

“This will be a hugely damaging white elephant. It just doesn’t make sense. Bathampton Meadows lie in a flat valley that are clearly visible from all the hills around,” she said.

“And they’re a natural sponge for the flood waters that are increasingly becoming part of our lives. Even the Romans knew not to build on them. I cannot believe that our current leaders are being so shortsighted.”

Traffic in Bath, one of the world’s most popular tourist destinations, has troubled politicians and local people for decades.

The geography of the city, nestling in a valley surrounded by hills with the Avon river running through, has made it difficult to find a way of getting 4 million visitors a year – on top of commuters and residents – in and around its Georgian streets.

Piers Taylor, a Bath-based architect and presenter of the BBC2 series The World’s Most Extraordinary Homes, insisted the scheme was not right. He said: “If this park and ride is built, we will destroy a vital aspect of Bath for ever.”

Steve Horler, a farmer who has land at Bathampton, pointed out that he had been refused permission to build two shepherd’s huts on the meadows because such a development was not deemed appropriate.

He said: “You could not make this up. They told me these two small huts were inappropriate. But yet they’re proposing to build a park and ride here.”

The campaigners say as well as ruining the meadows, which are mentioned in the Domesday Book, a park and ride will put bus services for the wider public at risk. They argue that people will drive to the park and ride rather than use local buses – which will then be cut.

But the council says park and ride forms a key part of its wider plan to improve transport, tackle congestion and support the continued growth of the city and local economy, which includes plans for about 7,000 new homes and 11,000 jobs in the city by 2035.

It says every day more than 73,000 people travel into Bath by car, a figure predicted to rise to 96,000 people by 2029.

The council leader, Tim Warren, said: “Bath’s economy is set to grow significantly in the coming years. We have to plan now for how people will get into the city in future without causing gridlock on Bath’s already congested roads.”

The council – which has park and rides to the north, south and west – said the new scheme to the east would be “sensitive to the local environment with minimal visual impact”.

Anthony Clarke, the cabinet member for transport, said: “Demand for our park and ride services continues to grow as more and more people want to get into Bath to work and visit. Addressing the notorious transport issues to the east of Bath is therefore critical to supporting the long-term growth of the city as a whole.

“This is also part of our wider strategy to improve transport in and around Bath that includes greater provision for cycling and walking and better rail services.

“If we do not take the action needed now, and provide alternative ways for people to get into and out of Bath without using a car, then traffic congestion will only become even worse in the years ahead.”