A government efficiency drive aimed at slashing spending in town halls and boosting productivity in the health service is likely to deliver billions of pounds of new business for private companies, the Guardian has learned.

Outsourcing firms are preparing for a bonanza of local authority contracts to provide everything from bin men to back office bureaucrats and have reported a doubling in the number of deals on offer this year. Private health companies are also expecting to earn billions of pounds from the planned overhaul of the NHS in which GPs would take over responsibility for spending £70bn.

Executives at Capita, the UK's largest outsourcing firm, said the number of opportunities for local authority contracts has already doubled this year and they see the healthcare market as "vast and potentially lucrative".

Richard Marchant, head of local government strategic partnerships at Capita, an FTSE-100 company which already works for councils in Harrow, Swindon, Southampton and Sheffield, said: "A major problem for the public sector is, we feel, a significant opportunity for us. Opportunities are at their highest level in two to three years. This year we have probably seen a 100% increase in opportunities [compared with 2009] and I suspect we will see another 50% increase in the following year."

Such an increase could deliver a £60m boost to Capita's revenues while councils are anticipating a 30% budget cut over the next four years. Other firms vying for town hall contracts include Serco and Mouchel.

The private sector boom comes amid the toughest financial climate for public services in a generation, and despite continued assurances from ministers that reforms to public services are aimed at achieving greater value for money and improving efficiency. Councils are braced for the biggest cuts to their budgets since 1945 and the growth in the market for privatised services has provoked anger that private shareholders, rather than taxpayers, are likely to benefit from efficiency savings that come from cuts.

Andy Burnham, the shadow health secretary, said: "Some private operators are going to have a field day, making a fortune from a system which will offer less public accountability." The appetite for outsourcing is so great that private firms are even vying to help set the curriculum and educational ethos of academy schools.

"If you can provide a better service at a lower cost surely the taxpayer should get the benefit, not a shareholder," said John Seddon, director of Vanguard Consulting, who argues against conventional outsourcing. "The truth is many outsourcing contracts ensure costs remain high."

Tonight the communities department conceded that badly drafted outsourcing contracts could "end up costing the taxpayer more" but insisted they could "help councils save money which can be reinvested in improving other services or helping keep council tax down".

"The private sector likes the clarity it has seen from the new government," said James Hulme, spokesman for the New Local Government Network.

"It will see the present climate as a greater opportunity than over the last couple of years even though the budgets are shrinking. The low-hanging fruit have already been picked in terms of rubbish collection and street cleaning.

"The services that are now likely to be privatised are those such as probation and care homes, and the public will feel a different emotional attachment to them."

The potential volume of work is so great that firms from India and Germany have entered the market, which could ultimately mean some town hall functions being carried out abroad.

"We are expecting more deals to come," said Rainer Majcen, managing director of Arvato, a privately owned German outsourcing firm that already has contracts with East Riding of Yorkshire and Sefton councils.

The US health giants Humana, UnitedHealth, Aetna and MCCI are all understood to be interested in healthcare contracts that could flow from a new commissioning system in which GPs may be given the power to buy in services from any health group or hospital that is properly accredited.

Minnesota-based UnitedHealth has already become a key adviser to primary care trusts and is running two GP practices in Derbyshire and three in London.

"There could be a bonanza for private companies if these changes go according to plan," said Jonathan Jackson at the stockbroker Killik & Co.

Privatisation of healthcare is being opposed by the unions.

"Private health already has a small role in the NHS [providing 4% of services], but we don't want it to grow," said Karen Jennings a spokeswoman for Unison, the public services union.

"The danger is that private companies will become so powerful that they will be able to determine what services are provided and how much they charge."