An inquiry into the building defects that forced the closure of 17 Edinburgh schools has "gone up a gear" as pupils return for the start of the new term.

Council leader Andrew Burns, who called for the inquiry, said the investigation could have implications for the wider construction industry.

He spoke on Wednesday as children started the new term following the earlier disruption, which was prompted by the collapse of a wall at Oxgangs Primary during stormy weather.

Around 7500 pupils and more than 600 staff had to be relocated in April while safety inspections and repairs were carried out.

Mr Burns said Scottish and UK ministers should scrutinise the findings of the inquiry, led by construction expert John Cole, when it concludes in December.

The Labour councillor rejected opposition claims the decision to fund the schools in a public-private partnership (PPP) contributed to the defects.

Similar defects in wall and header ties, which bind brick walls to the main structure, have been identified in other buildings including Lourdes Primary in Glasgow, which was not financed by PPP.

The affected capital schools were built by Miller Construction, which was acquired by Galliford Try in 2014, with maintenance provided by the Edinburgh Schools Partnership (ESP) and partner Amey BPO Services.

The council withheld payments from ESP while the remedial works were ongoing.

Mr Burns told STV News: "I'm very relieved to see that all 17 schools are fully operational from this morning. It's been a huge logistical effort to get them all back.

"I can only say thanks to parents, pupils and teachers for their forbearance. They are all safe but the detail of what's gone wrong will come out through the independent inquiry.

"It has started and will now go up a gear and will report back at the end of this calendar year. We intend to learn lessons from it, not just for Edinburgh but for the rest of the UK."

He said there were no indications exam results have been affected by the disruption.

Meanwhile, it emerged on Wednesday that a trade union coalition has written to First Minister Nicola Sturgeon urging her to hold a Scotland-wide inquiry into PPP.

Signatories include the Scottish Trades Union Congress (STUC), Unite, Unison Scotland, NASUWT, EIS general secretary Larry Flanagan and the Common Weal think tank.

Mr Flanagan said PPP levies "ongoing exorbitant costs to the public purse, when all available money should be channelled into supporting already stretched services".

Dave Watson, head of policy at Unison Scotland, said a wider inquiry "should look at the prospects for ending existing contracts using low public sector borrowing costs".

Pat Rafferty, Unite's Scottish secretary, said: "We need our MSPs to seriously consider the option of cancelling or renegotiating unfair and extortionate PFI contracts, and we need to make sure that the private finance alternatives put forward by the Scottish Government will really deliver value for money."

Joel Benjamin, campaigner for the UK-wide campaign group People vs PFI, said: "Scotland has 40% of UK PFI schools, with just 8.5% of the UK population."

He added: "PFI is a national scandal, the faults identified in Edinburgh can be found in schools, fire-unsafe hospitals and other public infrastructure throughout England and Wales.

"PFI is a failed model, it's time for a national inquiry to lift the lid on these secretive contracts."

Scottish Conservative education spokeswoman Liz Smith said: "Almost three years ago, we asked the Scottish Government to consider making changes to the school inspection process.

"Two cabinet secretaries dragged their heels, intimating they would review matters, but it now seems nothing is happening on this front.

"The debate about school buildings is not just about the future structure of contracts. There are other things that can happen now and the SNP should act decisively to make these changes."