Staff and pupils at four crumbling schools in the Bradford district must wait many more months to learn when rebuilding work will finally start.

Belle Vue Boys’ School in Heaton, Carlton Bolling College in Undercliffe, The Samuel Lister Academy in Cottingley, Bingley, and Oakbank School, Keighley, are all described as a “priority” by the Government.

Exactly one year ago, ministers pledged that a private finance initiative (PFI) scheme would be started to rebuild or revamp them “within the next year.” But a shortlist of bidders was announced only three weeks ago – and there is no date set for announcing the winner, or for the work to get under way.

Treasury sources say the procurement process is moving ahead only very slowly and that it could be the end of the year before the picture is clear.

Originally, the Department for Education (DfE) suggested many PFI schemes would go to market in 2012. Across England, work has started on only 29 of 261 “priority” schools.

Now a new £2bn scheme, to start next year, will see rundown schools rebuilt with public cash – abandoning the private finance model blamed for the slow progress. Tristram Hunt MP, Labour’s education spokesman, accused Education Secretary Michael Gove of diverting limited funds to his “free school vanity project.”

He said: “His Priority School Building Programme is decidedly not a priority – limping along at a staggeringly slow pace.”

But a DfE spokesman insisted there was no delay, saying: “This is usual for any procurement programme. This one is running faster than many others.”

And David Laws, the Schools Minister, said: “The programme is making great strides in ensuring that vital building work takes place at some of the schools in the worst state across the country.”

The four Bradford schools are in a “batch”, with Whitcliffe Mount Business and Enterprise College, Cleckheaton, All Saints Catholic College, near Huddersfield, and a seventh school in North Yorkshire.

The shortlisted firms to build them are BAM Construction Ltd, Morgan Sindall and Laing O’Rourke.

The DfE website reads: “The Education Funding Agency (EFA) will give further updates regarding this procurement on this page in the coming months.”

Ministers have vowed that all 261 “priority” schools will be rebuilt by 2017.

The new £2bn taxpayer-funded project offers hope to schools that lost their rebuilding cash when Labour’s Building Schools for the Future scheme was axed in 2010.