Charitable foundation Edutrust has submitted a formal "expression of interest" to sponsor – with the support of both Leeds's universities – an academy to replace Intake High School, the city's so-called "fame school".

Former pupils included Spice Girl Melanie Brown aka Mel B, Coronation Street, Cutting It and Waterloo Road actress Angela Griffin and Ivanhoe film star Steven Waddington.

The idea has taken a step forward with senior councillors agreeing to explore the plan in details and to carry out consultation.

They stress the move does not commit the city to the academy – a final decision will not be made until the results of the lengthy feasibility and consultation process are considered by the board in the autumn.

The Government wants local authorities to consider forming state-run independent schools wherever standards are not rising quickly enough.

Intake High has made steady progress since being removed from special measures in 2006, but the pace of improvement remains a concern, says the council.

An academy is likely to attract a £20million investment from the Government.

In opting to investigate the proposal, the council's executive board also considered a report outlining protocols which would ensure that any future academy in Leeds would remain a "full and active member of the Leeds family of schools."

Edutrust has already made a clear commitment to the protocols, which ensure cooperation from would-be academies with local authority arrangements on partnerships, governance, recognition of trades unions, admissions, exclusions and social responsibility.

Coun Richard Harker, executive board member responsible for learning, said: "We will consider any proposals which will bring rapid improvements while complementing the city-wide transformation of learning for all our young people.

"This move does not commit us to this specific proposal – if we don't feel it's the best option for this area then we will continue looking for one that is."

Chris Edwards, chief executive of Education Leeds, said: "We want to create brilliant learning places at the heart of all our communities, working in partnership with other local schools to give children and young people the chance to achieve their potential.

"We are happy that Edutrust appear to share our vision and are committed to our unique protocols to make academies work for Leeds."