The government has unveiled a sweeping strategy to create its own internal "cloud computing" system – such as that used by Google, Microsoft and Amazon – as part of a radical plan that it claims could save up to £3.2bn a year from an annual bill of at least £16bn.

The key part of the new strategy, outlined by the Cabinet Office minister Angela Smith, will be the concentration of government computing power into a series of about a dozen highly secure data centres, each costing up to £250m to build, which will replace more than 500 presently used by central government, police forces and local authorities.

The government will also push for "open source" software to be used more widely among central and local government's 4m desktop computers. That poses an immediate threat to Microsoft, whose Windows operating system and Office applications suite is at present firmly embedded as the standard on PCs in government, such as the NHS, which is one of the largest users in Europe.

But John Suffolk, the government's chief information officer, pointed out that cost savings of just £100 per machine would total £400m across government. Unlike Windows, open source operating systems such as Linux have no licensing costs and can be used on as many machines as required.

By 2015, the strategy suggests, 80% of central government desktops could be supplied through a "shared utility service" – essentially a cloud service resembling Google Docs, which lets people create documents online for free.

The move to a "government cloud" mirrors the system used by Google and other large companies, which put cheap "server" computers into huge data centres to provide computing power on demand which is delivered where it is needed via the internet. That would be provided to government departments and local government, replacing the ageing and inefficient systems used in many of the hundreds of data centres presently used – and frequently run at far below their capacity because they are dedicated to one department.

Suffolk said that "as a rule", UK citizens' personal data will not be transported overseas – although he could not rule it out. But security of data, and the data centres, would be a high priority, he said. He did not rule out using Google's or Microsoft's new cloud services: "We will see if they fit our business requirements and personal data requirements," he said.

Similarly the new "cloud" system will not include the security services such as MI5 or MI6, which have their own, separate systems.

Estimates prepared for the government suggest the "cloud" system could save £900m in their first five years, and £300m annually after that compared to the present structure.

The government also wants to build its own "app store" of software to solve frequently-seen problems, by re-using programs that have been written elsewhere and can be re-applied. "In government I've seen innovations where we have cracked hideously tough problems, but other parts of government are looking for the same solution and don't know it's there," said Suffolk.

Moving to a cloud-based infrastructure could cut costs of government computing significantly and also satisfy its drive for a "green" agenda by reducing power usage. The Inland Revenue, for example, is presently seeing huge demand for its online tax return system – but that peaks every January, and then drops substantially. A cloud-based system shared among departments could deal with such sudden loads while using less power, said Kate Craig-Wood, managing director of the hosting company Memset, who has been working with the government on the strategy.

"The good thing here is that the government has tried hard to involve small businesses," Craig-Wood said. She said that the new open source approach will benefit small businesses that want to bid for government contracts, and that it should lessen the number of big IT projects that are at risk of cost overruns: "The ability to take advantage of the cloud means you can build those projects up iteratively, which is how industry does it."

Smith admitted that the government had not always been quick to embrace new technology. "Back in 1885, the civil service bought its first-ever typewriter, despite stiff resistance from in-house calligraphers. About 20 years later the government took another leap into the unknown when it invested in its first telephone, a mere three decades after the technology was first demonstrated."

But telephones too could be revolutionised. The new scheme aims to replace many of the government's physical phone lines with internet-connected "voice over internet" (VoIP) systems by 2017.