The industrial action is set to take place next Thursday, and union leaders said today it will affect services "right across the board". About 8000 Unison members have voted by more than two-to-one in favour of the walk-out in protest at cuts and possible redundancies.

The savings are part of the authority's bid to save £10 million and the strike will coincide with a meeting where councillors are set to vote on measures to tackle the funding shortage. The council said the strike was "very disappointing" but it was essential that it balanced the books.

The union warned that, unless an agreement can be reached between now and next Thursday, the walk-out could be the first of many day-long strikes and boycotts. John Ross, Unison's service conditions convener based in Edinburgh, said: "Everything will be hit - social work, schools, housing, transportation, the lot.

"Many council staff are already under huge pressures to manage services without the resources they need. They cannot take any more and that is why our members have voted for action."

Council chiefs are desperate to plug the £10m hole in the council budget. It is expected that officials will attempt to recoup that money from cutbacks across a range of services - including the schools and nursery closures announced today. Though redundancies have not been listed as a definite option, council officials have refused to rule them out.

George Lee, Unison's Edinburgh branch secretary, said: "You cannot make cuts of up to £16 million without the threat of redundancies among the people delivering those services. Even at this late stage, council staff and their union have been kept in the dark about what the options are.

"The only thing the council has been clear about is that it cannot rule out redundancies."

But Unison leaders said they are still hopeful an agreement could be reached by next week to prevent the action. Mr Ross said: "I hope between now and next week we can have talks with the council on how this can be avoided."

Seventy per cent of Unison members who voted in the ballot agreed that strike action was the best course of action. To prevent disruption, the union is demanding assurances from the local authority that there will be no redundancies and no extra pressures on staff as a result of belt tightening.

A City of Edinburgh Council statement described the strike was "very disappointing news".

It said: "We greatly value our staff, appreciate the effort and commitment they give to providing services, and want to work with them to put the budget back on a sound footing again. The council faces a serious financial situation but we are determined to take the action necessary to address the overspend."

Councillor Cameron Rose, the Tory group's finance spokesman, said: "I think it is important for the people of Edinburgh we balance the budget and there are measures that need to be taken. I am not sure the Unison action will contribute to achieving this."