It is believed the proposal, which would have netted £40 million in savings by 2016-17, involved shutting about half of the 75 centres which exist to provide nursery education and health care for vulnerable families.

The idea reportedly provoked anger and disbelief when it emerged at a mammoth five hour Labour group meeting on Saturday Dec 1.

Councillors who were there have told Chamberlain News that Sir Albert failed to get approval to include the children’s centre proposals in a consultation exercise into the council’s £110 million spending cuts plan for 2013-14.

Sir Albert is reported to have explained that the grave financial pressures faced by the council and the need to cut spending by £600 million over six years meant that children’s centres in more affluent parts of Birmingham, including Sutton Coldfield, would have to go.

No vote was taken at the rowdy meeting, but when details for budget consultation were finally published on Thursday Dec 6 proposed closures had disappeared from the document to be replaced by a compromise £3 million savings plan.

This was made up of £2 million a year cuts from “non-core elements” of the children’s centres budget and £1 million from reductions to centres “applied with due regard to deprivation levels of the areas they serve”.

Sir Albert has also been forced on the back foot over growing concern among Labour councillors about the possibility of council refuse collection and street services being privatised.

It has emerged that a key condition of accepting a £30 million Government grant to introduce wheelie bins is to “market test” the council’s refuse service against those run by the private sector.

Sir Albert attempted to dismiss the privatisation claim at a cabinet meeting, although he stopped short of promising that refuse collection and street cleaning would remain in local authority hands.

A cabinet report into the wheelie bins proposal makes it clear that the council may have to give up direct control in order to get the grant.

The report states: “It is recognised that private sector providers can offer a wealth of experience and, on research evidence undertaken for the council, generally achieve efficiencies of about 10 per cent. It is intended to carry out a robust market testing exercise for the delivery of waste collection and street cleaning services.”