There needs to be "a big cultural change" towards sport in schools if Britain is to capitalise on Team GB's Olympic wins, David Cameron has said.
The PM called for a more "competitive ethos". Teachers said he was "shifting blame" for problems caused by cuts.
Later the BOA said 800 Olympic and Paralympic athletes would take part in a parade in London on 10 September.
Team GB have 22 gold medals, their best haul since 1908, but medal hopes in the individual showjumping were dashed.
All Team GB's Olympic and Paralympic athletes are due to parade from the City's Mansion House to the Victoria Memorial in front of Buckingham Palace the day after the Paralympics ends.
BOA chief executive Andy Hunt, asked why it was taking place on a school day, said: "We are trying to find a day that would work for everybody, to bring together what might be over 850 athletes, and then all of the other support staff, and make that happen across the both the Paralympic and Olympic teams was pretty challenging."
Sitting beside former Olympic silver medallist Amir Khan, Mr Cameron watched as Britain's Nicola Adams made her way into the flyweight final of the women's boxing.
Adams, from Leeds, beat India's Mary Kom and is on course for at least a silver medal.
But she said afterwards: "I want that gold. Words can't express how much I want it. To get that for Great Britain, that would just mean the world to me."
It is the first time women's boxing has been included in the Olympics.
In other developments:
- Up-and-coming Team GB hurdler Lawrence Clarke just missed out on a medal in the 110m hurdles, finishing fourth. He said afterwards he was pleased with his performance as he "didn't even expect to make the final".
- About 700 New Zealanders and their guests were evacuated from Kiwi House, after a gas canister being used for a barbeque exploded. Two fire engines put out the flames at the hospitality zone near Kings Cross. One person suffered minor injuries.
- Britain's women's hockey team will play New Zealand for bronze on Friday afternoon, after losing their semi-final 2-1 to Argentina.
- Sales of Paralympic tickets have reached a record 2.1m. London 2012 chairman Lord Coe said he was "absolutely delighted"
- Jamaica's Usain Bolt sauntered into the final of the 200m, where he will meet compatriot Yohan Blake, who won the other semi final.
- The evening session includes the men's boxing quarter finals
- South Yorkshire police said vandals had defaced winning heptathlete Jessica Ennis's gold postbox
- British BMX hopeful Shanaze Reade finished fifth fastest in the opening time trial
- Laura Weightman, from Northumberland, recorded a personal best but only qualified for the 1,500m final by nodding right on the line. She will be joined in the final by Britain's Lisa Dobriskey.
- seven athletes who have been missing
Speaking to LBC Radio after criticism of the government for approving the sale of 21 school playing fields, Mr Cameron said £1bn was being invested in school sports over the next four years.
But he added that more needed to be done to build a sporting legacy for British children.
"We need a big cultural change - a cultural change in favour of competitive sports," he said.
"The problem has been too many schools not wanting to have competitive sport, some teachers not wanting to join in and play their part."
But the general secretary of the National Union of Teachers, Christine Blower, said suggestions that teachers were letting the side down was "ludicrous".
"What we need is the support of government, not the shifting of blame," she said. "It's not because of teachers that funding for the School Sport Partnership has been so drastically reduced. Nor is it down to teachers that playing fields are being sold off, despite election promises."
Shadow education secretary Stephen Twigg has also criticised the government's decision to end the target of pupils doing two hours of sport a week, saying support structures needed to be place "at the grassroots" to "inspire the next generation".
Labour leader Ed Miliband said Britain needed to keep hold of "Olympic spirit" and the government had to do "a lot of thinking" about how it could make good on the promise the Olympics had given young people.
Olympics minister Hugh Robertson has said he is "pretty confident" sports funding can be maintained at the current level. He said elite sport was his priority, but that could not be guaranteed and "hard decisions" must be taken.
BOA chairman Colin Moynihan said: "Nobody is suggesting for a moment that every child wants to play competitive sport, that would be inaccurate. But there are hundreds of thousands of children who would love to take the inspiration they've got from either watching these Games or learning about them, they'd just love to translate that into the opportunity."
In showjumping on Wednesday, British trio Scott Brash, Ben Maher and Nick Skelton - fresh from their team title - missed out on the individual gold medal, which was won by Switzerland's Steve Guerdat.
Meanwhile London 2012 officials are refusing to confirm announcements from Muse and George Michael that they will take part in Sunday's closing ceremony.