Great Britain are on course to win more medals in Rio in four years' time than they did in London, according to the funding body that underpinned the nation's best Olympic performance in more than a century.

No host nation has managed to avoid a drop off in its performance at the Games that followed but UK Sport's chief executive, Liz Nicholl, said there was "no reason" why Team GB could not better its London medal haul of 65 in Brazil.

Peter Keen, the former UK Sport performance director who devised its "no compromise" strategy, also said it was "game on" to improve on the London medal tally in 2016.

"More medals is entirely possible," said Nicholl. "That is something we would want to commit to. If the system gets better, there's no reason why we can't get more medals."

Keen said: "There are so many things we can improve, whether that's governance or coaching. If we apply the knowledge we've got, there's no reason we can't get more medals. It's absolutely game on."

If ministers get their way, it could be that Lord Coe, who delivered London's successful Games, will lead the most successful British team in 104 years into the next one. Ministers are understood to be keen that Coe becomes the next chairman of the British Olympic Association, after Lord Moynihan announced he would step down a year early in November.

UK Sport hailed the success of Britain's Olympians, who exceeded its pre-Games target of at least 48 medals and at least fourth place in the medal table. After they had won their last medal, in the modern pentathlon on Sunday, the count stood at 65 – the exact number that Keen privately predicted before the Games. They finished behind only the USA and China in the medal table.

In public UK Sport would say before the Games only that it hoped to win between 40 and 70 medals and finish at least fourth in the medal table. It set 48 as the baseline. "We knew top four was a possibility; we knew we could challenge the Russians," said Baroness Campbell, the chair of UK Sport. "We can truly say this is the most successful Olympic team ever and the high performance system here is clearly working. Our no compromise approach clearly is working. We're proud of the athletes and we're proud of the sports."

In Beijing athletes won 47 medals in 12 sports. Officials took heart from the fact that Britain won medals across 17 sports in London and that the sports that have delivered the lion's share of medals over recent years – cycling, rowing, sailing – continued to succeed.

The government this week promised to maintain investment in elite sport at roughly the same level for the Rio cycle, by putting £508m into UK Sport over the next four years.

UK Sport is reviewing funding levels for every sport. As revealed by the Guardian in June, sports that qualified for London only because they were awarded home nation places are likely to see their funding cut altogether unless they can prove they will qualify for Rio, perform creditably and be in with a good chance of a medal by 2020. The vulnerable sports include synchronised swimming, beach volleyball, basketball, table tennis, judo, handball, indoor volleyball, water polo, rhythmic gymnastics and weightlifting. "We will not be able to fund every sport," said Nicholl. "Our aim is to make sure that we invest in every sport with medal potential. That for us is an absolute minimum. The starting point for handball and other sports with host nation places is to demonstrate they can qualify by right for the Olympics. If they can't be there, we can't invest in them.

"A sport like handball has been able to raise its profile like never before. It should be able to attract interest from the general public and corporate sponsors. Every sport must be responsible for growing itself to the point where it can get a medal. We'd love to see it come through to a position in future where they could qualify by right."

Every sport must submit a revised business plan by October in light of their performance at the London Games and the UK Sport board will decide how to allocate its funds on 12 December.

Ministers, keen to create a more joined-up approach across British sport and replicate the success at the elite end in community sport, hope Coe will consider becoming the BOA chairman after the Paralympics.

The move would be compatible with a portfolio of other business and sporting interests and wouldnot necessarily preclude him also running to be president of the International Association of Athletics Federations when that job becomes vacant in 2015.

Coe has agreed to become a part-time "legacy ambassador" to the coalition government, but ministers are keen for him to take on the BOA role. They also hope to persuade Sir Keith Mills, the deputy chairman at Locog, to take on a dual role as chair of UK Sport and Sport England.

Plans to merge the two bodies have been put on ice, but a joint chairman could be an option to try to get the two bodies to work more closely together and maximise their commercial income.