UK private schools could lose millions of pounds in business rate relief if they don't do more to help children from state schools, Tristram Hunt has warned.

The Shadow Education Secretary said a Labour government would restrict the tax relief unless independent schools lent teaching staff and helped state school children with university admissions as well as running joint curricular programmes.

Hunt, writing in the Guardian, promised that Labour would introduce a School Partnership Standard (SPS), which would require all private schools to form "genuine and accountable" partnerships with state schools, or risk losing tax breaks worth up to £700m ($1,097m, €883m) over the next Parliament.

Labour would introduce the legislation by amending the 1988 Local Government Act.

"We will encourage each institution to reflect on the skills, traditions and educational needs of their locality, and then develop an action plan to deliver tangible reform," the Shadow Education Secretary said.

"We want to see more private schools running summer schools, sponsoring academies, assisting state boarding schools and assisting professional exchange."

In total, 2,570 fee-charging schools can currently claim up to 80% in their business rates due to their charitable status.

Private schools saved more than £164m last year thanks to business rate reliefs, according to the Government's Valuation Office Agency.

But the Independent Schools Council (ISC) said 90% of its schools already work in close partnership with state schools.

The organisation's chairman, Barnaby Lennon, argued that the stripping of business rate relief would be a "very ineffective" tool to improve social mobility.

Hunt also said that private schools should compete with state schools at sport and debating.

"It baffles me that we can have private schools loaning a sports pitch to the local comprehensive once or twice a year yet completely refusing to play them at football or opening up their halls and amphitheatres yet unwilling to engage in a debating competition," the Shadow Education Secretary said.

"Social enterprises such as Debate Mate have shown how rewarding and relatively easy it is to set up debate clubs in high disadvantage state schools. And it is hardly difficult to join the local sports leagues.

"I see absolutely no reason why private schools should persist with their exclusive private-only competitions."