Airlines are failing to take up the most efficient planes in sufficient numbers to make a significant dent in their carbon dioxide emissions, a new study has found.

The most efficient new aircraft models, such as the Boeing 787-9 and Airbus A350-900 and A320neo, can achieve substantial carbon savings over older models, but no airlines have invested sufficiently in the new types to reach the top levels of energy efficiency, according to a ranking by Atmosfair, a German NGO.

In the annual Atmosfair Airline Index for 2018, published on Saturday, no airlines received an A for efficiency, and only two airlines were ranked in efficiency class B.

TUI Airways, the British holiday airline, came top of the rankings for the second year running, reaching just under 80% of the possible optimum level of carbon emissions. TUI Fly, the company’s German counterpart, came in fourth.

Atmosfair also found that only one in 10 airlines worldwide were succeeding in keeping their greenhouse gas emissions constant while achieving economic growth. Among these were Thai Airways, Finnair, American Airlines and All Nippon Airlines.

Dietrich Brockhagen, executive director of Atmosfair, said: “Our results show that the efficiency improvements of the vast majority of airlines worldwide is not sufficient [to keep within the] 2C or 1.5C target [of the Paris agreement]. We need new, synthetic and CO2-neutral fuels and other more radical measures to curb CO2 emissions in the sector.”

British Airways was placed at 74th, with an efficiency rating of D, behind companies such as Aeroflot and Aeromexico. It fell behind many of Europe’s other flag carriers, including Alitalia, Lufthansa, Air France, KLM and Iberia.

British Airways said: “We are committed to reducing our carbon emissions and have improved efficiency by more than 10% since 2008. We are well on course to deliver a 25% improvement in carbon emissions reduction by 2025. British Airways is the first airline in Europe to invest in building a plant to generate renewable jet fuel from household waste, and last week we kicked off a research project with some of the UK’s leading universities to find a way to power a long-haul aircraft with 300 customers on board with zero emissions.”

Facebook Twitter Pinterest Virgin Atlantic chairman Sir Richard Branson co-founded the Carbon War Room, which since 2009 has operated as a non-profit organisation aimed at speeding up the adoption of cleaner, low-emissions technology by businesses. Photograph: Hannah McKay/PA

The company also pointed to a commitment by its parent group IAG to invest $400m (£313.6m) on alternative sustainable fuel development over the next 20 years.

Virgin Atlantic Airways ranks 83rd in the world, behind many airlines from developing countries such as Indonesia’s Garuda, Royal Air Maroc, Air India, and Taiwan’s Eva Air. This showing comes despite the much-publicised activities of Sir Richard Branson, Virgin’s chairman, in highlighting the risks of climate change.

Branson co-founded the Carbon War Room, which since 2009 has operated as a non-profit organisation aimed at speeding up the adoption of cleaner, low-emissions technology by businesses.

Virgin took issue with the report methodology, saying it misrepresented the airline. A spokeswoman added: “We have undertaken a massive renewal programme to replace our entire fleet over a 10 year period, switching from four-engine aircraft to much more efficient two-engine aircraft. As a result we have reduced our aircraft carbon emissions by 23.7% since 2007. Our carbon emissions will continue to reduce as we take delivery of more new aircraft over the next three years.”

Carbon emissions from airlines grew by about 5% last year, while the number of kilometres flown increased by 6%, according to Atmosfair, showing that much more needs to be done to ensure aviation does not take up an unsustainable amount of the world’s remaining “carbon budget”. Biofuels are being given trials as an alternative to fossil fuels for aviation, but these carry their own difficulties, not least the threat of deforestation. Virgin recently used recycled waste to fuel a flight, a potentially more environmentally sound alternative.

“You cannot beat physics, therefore long-haul flights will not be feasible with heavy batteries and electric engines,” said Brockhagen. “But you can produce carbon neutral kerosene synthetically, using carbon extracted from the air, water and green electricity. This is ready technologically, but 10 times more expensive per gallon than fossil kerosene. Who will invest the billions to scale this technology up? If airlines grouped together they could do it, but this would require an international spirit of cooperation over competition, so far rarely seen in the industry.”

There are also ways for airlines to reduce their emissions without resorting to new fuels and planes, through adjusting their pilots’ flying practices and small tweaks to planes. Some airlines look to offset their emissions through carbon reductions elsewhere.

A spokesman for Airlines UK, which represents the industry, said: “UK airlines are making enormous efforts to reduce their carbon emissions, and are committed to a global target to cut CO2 emissions from all flights by 50% of their 2005 levels by 2050, through technology, operational efficiency improvements and the use of sustainable biofuels. On top of this, in 2016 the International Civil Aviation Organization adopted the Carbon Offsetting and Reduction Scheme for International Aviation to address CO2 emissions from international aviation – a global first for any sector.”