A “jet-setter” tax on Europe’s frequent flyers could slow global heating and raise €64bn (£54bn) a year at no extra cost to most people, a report has found.

Carbon pollution pumped out of planes could fall by 21% if people were made to pay more for each extra flight they take beyond the first return trip, according to analysis from the New Economics Foundation (NEF) and partner organisations. Just over half the benefits in a given year would come from the 5% of people who fly the most, while 72% of people would escape fees by flying once or not at all.

A frequent-flyer levy would raise cash that could be invested in trains and buses while reducing “excessive” flights for the wealthiest, said Magdalena Heuwieser from the campaign group Stay Grounded, which co-wrote the report. “Right now, it doesn’t matter whether you’re flying to visit your family for the first time in years or taking a 10th annual flight to your luxury house on the coast – you’ll be paying the same tax for that flight.”

The report, shared exclusively with the Guardian, is the first to explore how a frequent-flyer levy could work in Europe.

Researchers from CE Delft modelled the climate effects of a staggered tax on flights and found the proposal would reduce passenger numbers in 2028 by 26% and emissions by 21% from a business-as-usual scenario.

The levy would start at zero for the first return flight in 12 months and rise by €100 for each return trip, with surcharges for longer distances and first class travel.

AdaStone Law explored the legal implications and concluded the proposal was feasible under EU and national laws, though strict data privacy laws could cause problems when ticket sellers display prices to customers.

Rich people would be most affected because they fly more often, an analysis of polling data from More in Common shows. It found only 15% of households with a yearly income below €20,000 flew enough to pay the proposed levy, rising to 63% of households with an income above €100,000.

“We love flying and the planet but our freedom to continue flying in the future is now under threat,” said Finlay Asher, an aerospace engineer and cofounder of Safe Landing, a campaign group made up of aviation workers pushing the industry to act in line with climate science. “It will be impossible to set ourselves on a new trajectory of rapid emissions cuts without focusing on frequent flyers, who are responsible for the majority of our pollution.”

Emissions from aviation are rising but flights remain heavily subsidised across the continent. Jet fuel is exempt from fuel duties, plane tickets are usually exempt from VAT, and most flight emissions are left out of the EU’s emissions trading scheme, which puts a price on planet-heating pollution.

Marlene Engelhorn, an Austrian millionaire who is giving away 90% of her wealth, said it was time to harness the “unnecessary destruction my class’s jet-setting causes” and demand they contribute to the costs of saving the planet. “The mile-high club of private planet combustion, where wealthy people like me can ferment in our comfort zones, needs to close its doors.”

The report found an EU-wide levy would be an ideal instrument to tackle the sector’s rising pollution, though it would require unanimity among member states, which has proven particularly hard to achieve on tax policy. It suggested individual member states or small alliances of countries could take the first step but did not explore which might do so or how such actions would distort the market.

Energy experts have identified synthetic fuels, electric planes and more efficient operations as promising solutions to decarbonise aviation but say the technological hurdles are far greater than in most sectors of the economy.

They have proposed policies to tackle the growing demand for flights, and highlighted the disparity in aviation emissions that extends well beyond the private jets of the super-rich and the business travel of corporate elites.

“Those of us who fly more than one or two times a year should recognise that we are a very small subset of the world’s population – and consuming the climate budget at the stake of others,” said Sola Zhang, an aviation expert at the International Council on Clean Transportation, who reviewed an early draft of the report but was not involved in writing it.

“Flying less or shifting modes is obviously the most effective solution,” she said. “For flights that are still taken, supporting the transition to zero-emission aviation is the second best option.”