Police forces across the region are facing immediate cuts of almost £9 million.

But Police Minister Nick Herbert, who ordered the cuts, said they should not hit the frontline fight against crime.

However, a West representative of rank-and-file officers said that was "nonsense" and warned of much worse to come.

The government announced on Monday the first £6.2 billion of cuts it was planning in this financial year, to start tackling Britain's debts.

Yesterday Mr Herbert said the Home Office share was £367m, and it would target overheads and waste, including significant cuts to travel, marketing costs and consultancy services.

He said police forces in England and Wales would suffer £125m cuts, with each constabulary losing the same percentage of funding.

It means South West forces will see their general grants reduced by a total of £8m, with another £800,000 going from the budgets for buildings and equipment.

He is also slashing £10m from the police budget for fighting terrorism.

Mr Herbert said in a statement to MPs: "I am confident that savings of less than one per cent of expected spending in 2010-11 by police authorities can be made while maintaining a frontline policing service."

He warned he expected "forces to be held to this" by police authorities and the Inspectorate of Constabulary.

Alex Duncan, secretary of Avon and Somerset Police Federation said: "There is no way they can implement this kind of cuts and guarantee it will not impact on frontline services.

"I recognise the difficult economic times, but to receive these further cuts is a real blow."

He told the Western Daily Press there were real efficiency savings that could be gained from policing, such as having standard uniforms, vehicles and IT solution.

"But to take a funding formula that is flawed to start with and has persistently under-funded Avon and Somerset and to announce there will be no impact on frontline services is nonsense," he added.

"It is not a happy day, and most of us would be astounded if this was the last of it."

Gloucestershire Police – who last month announced an end to a recruitment freeze in order to protect the number of bobbies on the beat – will have to find £1 million of cuts.

Avon and Somerset Police will lose almost £3m, and chief constable Colin Port and police authority chairman Moira Hamlin said: "We are already the second worse-affected force in the country in the way that the funding formula is implemented."

Police in Wiltshire will lose £1.1m.