The Premier League has agreed to expand its school sport programme to every primary school in England and Wales as part of a grassroots sport initiative.

The school sport programme is currently in 4,158 schools but the league is to more than double its reach to 10,000 schools in the next three years and extend it to all primary schools within six years.

The programme, which involves both Premier League and Football League clubs’ community coaches, offers PE lessons and teacher training in addition to the government’s £150m a year school sport premium, as well as after-school multi-sport clubs and tournaments that encourage competitive sport.

The prime minister, David Cameron, said “Every child should have the opportunity to play sport, benefit from great coaching and be part of a team.”

The Premier League’s executive chairman, Richard Scudamore, said “The Premier League and our clubs have always accepted that with success come responsibilities to the communities that sustain the game – last season more than half a million young people took part in Premier League-funded community programmes.

In February, all 20 of our clubs agreed to increase the amount we commit to a range of good causes, especially those involving young people”.