The British Infrastructure Group (BIG) claims the tax acts directly against a policy of extending UK business links to the "farthest reaches of the globe".
The tax is set to rise again in April to £150 for some long-haul flights.
Opponents accused the aviation industry of wanting a "free ride" on air taxes.
In its report, BIG said air passenger duty (APD) should be cut by 50%, then scrapped altogether.
Grant Shapps, the former international development minister who leads BIG, said Prime Minister Theresa May needs to make good on a promise she gave on Monday to "forge a bold, new, confident future for ourselves in the world".
He said: "Particularly post-Brexit, now is the time to do it."
He added that reducing APD could provide an immediate "Brexit dividend" because the government would not have to wait until Article 50 is triggered to make the cut.
Britain has one of the highest air travel taxes in the world.
On economy class flights of over 2,000 miles, passengers pay £73 in tax, which will rise to £75 next year. On long-haul business class journeys, flyers currently pay £146 in duty which will increase to £150 in April.
In the report, BIG cites industry figures that show UK APD for non-economy tickets is three times more expensive than France and four times higher than Germany.
It notes that Ireland has scrapped APD completely. Also, Scotland is planning to reduce APD by 50% in 2018.
"APD has disproportionate effects on different tickets, disadvantaging flights to the Far East and especially to developing economies, where the cost of a plane ticket from London can be well over 10% tax," the report said.
"If the government is to act on its commitments, especially those of securing new trading partners outside the EU, it must make it as easy as possible to do business, conduct negotiations and to stimulate the exchange of people and skills.
"It cannot continue to actively make extra-European travel more expensive than it needs to be."
Some MPs will strongly resist any attempt to cut aviation taxes.
Earlier this week, the Environmental Audit Committee said the Treasury must consider the environmental impacts of its decisions.
They are likely to point out that the biggest beneficiaries of a duty cut would be long-haul holiday makers, who might otherwise be spending their money in the UK.
Business passenger numbers are stagnant - the growth in demand is for holidays.
They will mention that aviation is already uniquely protected from efforts to cut carbon emissions: under the government's plans, emissions from motoring and home heating will have to be cut to accommodate the growth in carbon dioxide from aviation.
Critics are also likely to say that families travelling by air pay less tax per mile than car drivers, even though driving a family on holiday causes less pollution than going by plane.
They will also question whether £150 tax will really deter a company director who has forked out for a business class seat.
While the former Chancellor George Osborne exempted children under 16 from APD, the tax has continued to rise for adults.
When it was introduced in 1994, the charge was £5 on short-haul flights and £10 on long-haul travel and was expected to generate £330m a year in revenue.
APD now generates around an annual £3bn for the government.
Mr Shapps argued a sharp drop in tax revenue from implementing a 50% cut would be recovered from increased trade outside Europe.
He added that a reduction would allow Philip Hammond to "stamp his own authority" as chancellor in his first Autumn Statement next Wednesday since being appointed to the role.
However, Mary Creagh MP, chair of the Environmental Audit Committee, said: "Transport is the highest emitting sector of the UK economy and there are already problems with the UK meeting our fourth carbon budget which starts in six years.
"We recommend that the chancellor green check all Autumn Statement decisions, especially any change to air passenger duty which could increase airport congestion and air pollution."
John Stewart, from pressure group HACAN, said that every year before the Autumn Statement, calls are "trotted out" for an end of APD.
"Every year key facts are glossed over. For the vast majority of passengers it adds just £13 to a ticket, less than the cost of  breakfast at an airport terminal.
"The aviation industry enjoys tax-free fuel.  If its fuel was taxed at the same rate as petrol for cars, airlines would end up paying much more than they do through APD."
Labour's environment spokesman Barry Gardiner MP said: "Aviation needs to follow the polluter pays principle.
"BIG are being disingenuous in claiming reduced tax is necessary for trade: any business committed to exporting to China isn't going to measure the cost/benefit in terms of £150 air passenger duty".
A Treasury spokesperson said: "We keep all taxes under review, and do not comment on speculation around the Autumn Statement."
MPs are urging the government to halve air passenger duty in next week's Autumn Statement, saying the tax hampers post-Brexit Britain's ability to trade outside Europe.