The National Audit Office (NAO) has confirmed that it intends to conduct an investigation into Ofcom's recent auction of 4G spectrum, to see whether it achieved the best possible return for the UK economy.

The sale of British airwaves raised £2.3 billion for the public purse - £1.2 billion short of the £3.5 billion predicted by Chancellor George Osborne, and also below the £4 billion analysts had estimated based on prices fetched in recent European 4G auctions.

The NAO's auditor general, Amyas Morse, has now written to Labour MP Helen Goodman, saying that he intends to conduct a value for money study of the auction. The NAO is currently scoping the study, and will announce shortly on its website what it will cover and when to expect the report.

Ahead of the auction, Ofcom chief executive Ed Richards had distanced himself from the government's claims that the sale of 4G spectrum would raise £3.5 billion, claiming that the first time he heard the figure was in the Autumn Statement.

At a press conference in December, Richards said that Ofcom would not attempt to predict how much the sale of 4G spectrum would raise, adding that revenue maximisation was not the objective of the auction. The reserve price was set at £1.3 billion.

"We will be judging the auction ourselves on whether we believe it has successfully produced an efficient outcome, in which the bidders were able to express their preferences thoroughly and clearly and effectively during the process such that we're confident that the spectrum will be used in the most efficient way," Richards said at the time.

"However many billions the actual revenue is, the real economic benefit here is in the benefit to consumers and the the economy from the deployment of these highly valuable services. If we were to calculate the estimated economic benefit of that, it would massively dwarf the revenues from the auction, so that is the game for us."

In a letter to Morse, however, Goodman said that by not making maximising the auction's revenues an objective for Ofcom, the government had failed to get value for money.

"It is entirely right that the National Audit Office has launched this investigation. Serious questions must be answered as to why the Conservative-led government ended up £1 billion short of the estimate George Osborne had provided just months earlier," Goodman told The Guardian.

"When the 3G auction took place, Labour ensured that maximising revenue was an objective. The Conservative-led government did not do the same for the 4G auction, which I believe was a serious mistake." The 3G auction in April 2000 raised £22.5 billion.

Commenting on the news, analysts at Espirito Santo said that the issue is contentious, as the forecast proceeds of £3.5 billion were included in the government finances in the Autumn Statement last December, and have effectively already been spent.

"This investigation is a questionable use of public funds, in our view - the structure of the auction was set up to ensure four credible national wholesale mobile operators (notably reserving spectrum for the fourth largest operator, Three UK), not to maximise revenues for the Government. We believe the Government was being over-optimistic in its forecasts."

As yet, no new 4G services have gone live as a result of the auction, although the UK's largest operator EE is already providing 4G in 50 towns and cities using its re-farmed 1800MHz spectrum.

O2, Vodafone, Three and BT are expected to launch their own 4G services using the newly auctioned 800MHz and 2.6GHz spectrum in the summer.