The levels of funding for elite sport which has seen Britain achieve extraordinary Olympic success may be reaching an end, with a dramatic fall in the National Lottery ticket sales creating a possible £30m reduction for the next four-year cycle.

Sports such as swimming, cycling and rowing, which had been expecting to hear from UK Sport a week on Thursday that their success at the Rio de Janeiro Olympics would bring an increase in funding for Tokyo 2020, are instead likely to be told that there will be less money available. It is understood that UK Sport have already appealed to the Treasury for special dispensation on funding but been turned down.

The organisation, which has built a sporting machine out of lottery funding, will now appeal to Prime Minister Theresa May, though the prospect of a bail-out seems remote, with the UK Sport meeting next Wednesday to agree the funding levels for individual sports.

UK Sport could offer no explanation of why fewer people are buying National Lottery tickets, though the decision by the BBC earlier this month so scrap the Saturday night National Lottery draw demonstrates that the fall-off is serious. The programme has lost 17 million viewers since it launched in 1994.

Carr said: “The issue for UK Sport is we have to make some difficult decisions. We anticipated there was going to be a tighter budget right back in the spring so we have sent expert groups into some of the sports to make sure they are driving the maximum efficiency.

“What everyone will see is that very many of the sports may well have less funding but that’s maybe because of the efficiencies that have been made. But if we don’t get a solution before next Wednesday from Government the reality is that yes we are going to have to make some hard decisions.”

Despite the huge feel-good factor created by the success in Rio, where second-placed Team GB beat China in the medals table, UK Sport’s position is made more difficult by the fact that the Government does not have substantial sums to throw around. “We understand. We are not stupid,” Carr said. “We know what’s going on. On the other hand it’s a relatively small amount of money, £6million or £8milliom a year.”

Lottery ticket sales fell by £226m from April to September this year compared with the same period last year, and Lottery operator Camelot warning of more falls to come, despite “encouraging signs of improvement” in the summer. The arts are facing the same struggle. The total amount returned to the arts from April to September this year has been £156.6m, down from £175m last year.

Team GB's Rio 2016 gold medals Show all 26 1 /26 Team GB's Rio 2016 gold medals Team GB's Rio 2016 gold medals adam-peaty.jpg Swimming, men's 100m breaststroke Getty Team GB's Rio 2016 gold medals joe-clarke-rio-olympics.jpg Canoeing, slalom K1 Jamie Squire/Getty Images Team GB's Rio 2016 gold medals diving-laugher-mears.jpg Diving, men's synchronised three-metre springboard Getty Team GB's Rio 2016 gold medals cycling-team-sprinters.jpg Cycling, men's team sprint AFP Team GB's Rio 2016 gold medals stanning-glover.jpg Rowing, women's pair Getty Team GB's Rio 2016 gold medals rowing-rio.jpg Rowing, men's coxless fours Getty Team GB's Rio 2016 gold medals team-pursuit.jpg Cycling, men's team pursuit Getty Team GB's Rio 2016 gold medals olympic-mens-rowing-eight1.jpg Rowing, men's eight Getty Team GB's Rio 2016 gold medals trott-gold-rex.jpg Cycling, women's team pursuit Rex Team GB's Rio 2016 gold medals mo-farah-13-8-2016.jpg Athletics, men's 10,000m PA Team GB's Rio 2016 gold medals max-whitlock.jpg Gymnastics, men's floor and men's pommel horse Getty Team GB's Rio 2016 gold medals justin-rose.jpg Golf, men's individual Getty Team GB's Rio 2016 gold medals jason-kenny-3.jpg Cycling, men's individual pursuit and men's keirin Getty Team GB's Rio 2016 gold medals andy-murray.jpg Tennis, men's singles Getty Team GB's Rio 2016 gold medals Dujardin.jpg Equestrian, individual dressage Arnd Bronkhorst/FEI Team GB's Rio 2016 gold medals giles-scott.jpg Sailing, men's finn Getty Team GB's Rio 2016 gold medals laura-trott.jpg Cycling, women's omnium Getty Team GB's Rio 2016 gold medals jason-kenny-2.jpg Cycling, men's keirin Team GB's Rio 2016 gold medals alistair-brownlee.jpg Men's triathlon Getty Team GB's Rio 2016 gold medals mills-clark.jpg Sailing, women's 470 Getty Team GB's Rio 2016 gold medals jade-jones-2.jpg Taekwondo, women's 57kg Getty Team GB's Rio 2016 gold medals nick-skelton.jpg Equestrian, individual jumping Getty Team GB's Rio 2016 gold medals hockey-gb.jpg Field hockey Getty Team GB's Rio 2016 gold medals liam-heath1.jpg Men's K1 canoe sprint final Getty Team GB's Rio 2016 gold medals nicola-adams4.jpg Boxing, women's flyweight Getty Team GB's Rio 2016 gold medals mo-farah3.jpg Athletics, men's 5,000m Getty

Camelot chief executive Andy Duncan recently said that “the current climate of economic uncertainty and signs that consumers are being more cautious with their spending” meant the next six months would be challenging. He also said that competing lotteries were also reducing National Lottery income.

British Olympic success has been the result of a focussed 18-year investment of National Lottery money. Joe Joyce’s boxing silver at Rio was the 700th by Olympians and Paralympians since lottery finding of the sports began in 1997.

With £274m doled out across all Olympic sports by UK Sport during the four-year Rio cycle, Britain’s 67 medals will have come at a cost of just under £4.1m each, at a time when participation in sport in the UK remains lower than it did when London hosted the 2012 Olympics.