UK Sport has been urged by the governing bodies of 12 British sports to end its funding policy that places heavy emphasis on medal success and apply "at least a baseline level of funding" to all Olympic and Paralympic sports.
In a letter sent to The Guardian, the dozen governing bodies also challenge UK Sport’s current consultation on future strategy.
The signatories are Archery GB, Badminton England, BaseballSoftballUK, British Fencing, British Handball, GB Luge, GB Wheelchair Rugby, Table Tennis England, British Volleyball, British Weightlifting and British Wrestling.
None of them will be funded during the Tokyo 2020 Olympic and Paralympic cycle.
"It seems designed to create fear that there will be a total collapse of the UK medal tally should the current funding model be meddled with," the letter reads.
"We believe that giving many millions of pounds to some sports but none to others is divisive and will prove self-defeating.
"We think the British public believes in fairness and equality of opportunity, and the best way to achieve this is to provide at least a baseline level of funding to all Olympic and Paralympic sports.
"We are confident that this can be achieved without sacrificing current medal success."
The group has also called for the criteria upon which funding is based to be changed.
"UK Sport has a responsibility to ensure that all our Olympic and Paralympic athletes are encouraged to achieve their potential and that a system of development opportunities should be there for all of them," the letter adds.
"The popularity and levels of participation of a given sport are key to inspiring a nation and must be considered when funding decisions are made."
Earlier this month, a 10-week consultation into how UK Sport distributes National Lottery money was launched.
It means the way elite sport is funded in Great Britain could be facing a major shake-up after Tokyo 2020.
Launched by the high-performance funding agency, the public discussions will look into UK Sport's future investment principles for Paris 2024 and how best to "inspire the nation through elite success".
The organisation invests around £100 million ($133 million/€114 million) of Lottery and Government money into high-performance sport each year.
Its "no-compromise" policy has been the driving force behind elevating Britain into one of the most successful Olympic and Paralympic teams since its launch following a disappointing performance at Atlanta 1996.
Then, Britain finished 36th in the overall medal table with only one gold.
The advent of Lottery funding, however, saw Britain finish 10th at Sydney 2000 and Athens 2004, fourth at Beijing 2008 and third at London 2012.
They then finished second at Rio 2016 with a total of 67 medals, including 27 gold, surpassing Britain's overall medal tally at its home Olympics four years earlier.
The approach has attracted criticism, however, especially from national governing bodies of sports which have failed to hit their medal targets and, as a result, have had their funding cut.
The consultation period will form the basis for a new funding strategy, due to come into effect from April 2021, when the current funding cycle for Tokyo 2020 finishes.
UK Sport has commissioned two sports consultancies - Future Thinking and The Sports Consultancy - to conduct and analyse the consultation responses, in order to keep the process "independent and impartial".