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The National Audit Office (NAO) will investigate the government's sale of super-fast 4G mobile phone spectrum after the money raised fell far short of forecasts.

The NAO said it would conduct a value-for-money study of Ofcom's auction.

This year's auction raised £2.3bn, which was £1.2bn less than the amount the chancellor said it would raise.

The NAO said it would shortly set out the terms and timing of the study .

George Osborne's Autumn Statement on the government's finances, which was delivered in December, included the figure of £3.5bn that he expected to raise from the spectrum sell-off.

It allowed him to maintain at the time that government borrowing was falling.

The amount was also far lower than the £5.2bn actually offered by all the bidders, as an eBay-type system was used, whereby the highest bidder puts on the table the maximum it is prepared to pay, but is required to pay only slightly more than the sum offered by the next highest bidder.

The NAO's move was prompted by a complaint by Labour MP Helen Goodman.

She was concerned by remarks made by Ed Richards, the chief executive of regulator Ofcom, which arranged the auction, to the effect that raising money was not the prime purpose of the sale.

Mr Richards told the ����ý at the time that the figure was lower because "we are in very, very different times", adding that maximising the size of the auction was not the objective it was set by the government.

He added: "What we were trying to do was ensure that a valuable economic resource was brought into productive commercial use."

The 4G auction sold off a large slice of radio spectrum to Everything Everywhere; Hutchison 3G UK; Niche Spectrum Ventures, a BT subsidiary; Telefonica (O2); and Vodafone.

4G is far quicker than the previous widely-used spectrum of 3G.

The auction of 3G, 13 years ago, raised £22.5bn, a far greater amount than expected at the time.