Four crumbling schools in Bradford and one in Cleckheaton will be rebuilt, ministers have insisted – but the projects face a delay of up to one year.

The DfE has announced that private cash would be sought to rebuild the schools “within the next year”.

They are Belle Vue Boys’ School, Heaton, Bradford, and Carlton Bolling College in Undercliffe, Bradford; Oakbank School, Keighley; The Samuel Lister Academy, Cottingley, Bingley, and Whitcliffe Mount Business and Enterprise College in Cleckheaton.

No start dates can be set for rebuilding work until the ‘batch’ is open to bidding by construction companies – which cannot happen until affordable finance is found.

Councils were asked to nominate the schools in most need of repair, and the Government sent surveyors to assess each bid.

The amount to be given to each successful school is still to be decided.

The DfE originally promised that some ‘batches’ would be released by the end of last year, but only one – in Hertfordshire and Berkshire – is ready.

And, in further worrying evidence that the revamped private finance initiative (PFI) is in trouble, the DfE has abandoned plans for the further 137 schools across the country.

Ministers have reluctantly accepted that no affordable deals are available, so the 137 are in a queue for direct grants, after 2015 – if cash can be found.

The switch is an embarrassment for Education Secretary Michael Gove, who originally vowed that 212 of his 261 ‘priority’ schools would be rebuilt using PFI.

Stephen Twigg, Labour’s education spokesman, attacked the lack of progress, saying: “This failure will mean pupils are stuck in overcrowded classrooms or under leaky roofs.”

All five schools which will get funding were promised help, from a £2.4 billion “priority” scheme, after many saw their dreams dashed when the Building Schools for the Future scheme was axed in 2010.

However, the DfE defended the latest hold-ups to its troubled rebuilding programme, insisting it was “making the right decision for the taxpayer”.

A DfE spokesman insisted progress would be made with the Bradford and Kirklees ‘batch’ within 12 months.

He said: “We always said this would be a five-year programme and we are still within that timetable.

“We are on schedule with those commitments. This announcement has not resulted in any delays.”