The jobs axe began to swing through Whitehall this week as the Department for Business, Innovation and Skills (BIS) and the Department for Education (DfE) launched voluntary redundancy programmes to trim administrative costs.

Up to 600 jobs could be on the line as a result of the redundancies which will take place before the government lowers the pay-off terms to civil servants. By applying for redundancy in this round, staff will receive the current terms – on average, the equivalent of three years' salary. The government wants to introduce terms similar to those in the private sector, where a one-year payment is more typical.

Whitehall sources reckoned that while BIS and the DfE have been quick to launch their redundancy schemes, others would follow in the days and weeks ahead. Neither department would disclose a target for cuts, though sources indicated both would be aiming for between 8% and 10% of staff. BIS employs 3,500 and education 2,600, which suggests headcount could fall by about 600.

The business department hopes to achieve £7m of cuts through its redundancy scheme, part of an effort to slash £38m from its annual budget. Other savings are being made by cutting travel budgets, using public transport when possible and a freeze on marketing budgets.

"We have said to staff that we are committed to maintaining a high level of performance," a BIS spokeswoman said.

The savings are being implemented before the chancellor sets out the precise cuts that will be applied to departments in the 20 October comprehensive spending review. However, George Osborne has outlined plans to make £83bn of savings by 2014-15, with £61bn from departmental budgets. A freeze on public sector pay has also been put in place.

The Whitehall redundancies are expected to be the tip of the iceberg as the government cuts costs to reduce the budget deficit with a view to ensuring the country keeps the triple A credit rating it needs to raise funds on money markets.

The Office for Budget Responsibility has forecast that 499,000 jobs will be lost in the public sector, though it emerged last night that this figure had been reduced by 175,000 after the team, led by interim head Sir Alan Budd, factored in assumptions about pension and pay.

The BIS job cuts may cause particular concern because the department, run by Vince Cable, has positioned itself as the "department for growth", aiming to rebuild manufacturing and kick-start apprentice training programmes.

Osborne's announcement of the 25% inflation-adjusted reduction in spending in government departments over the next five years had always been expected to hit BIS, although he had promised to protect spending on schools. Yet the education department has not avoided becoming one of the first in Whitehall to instigate a redundancy programme.

In June, education secretary Michael Gove was asked for an estimate of the redundancy costs in his department to which, according to the official parliamentary record Hansard, he replied it had "made no employees redundant". He said that its predecessor, the Department for Children, Schools and Families, had also not made employees redundant.

Gove went on to say: "The department is subject to the same recruitment restrictions as all other government departments. It has not yet identified any necessary additional reductions to its non-frontline staff and therefore cannot provide any estimate in relation to cost".

A spokesman for the education department declined to provide further details about the voluntary scheme.