The National Audit Office expects to deliver its verdict in July, head Amyas Morse told campaigning MP John Healey.
The Labour former minister led calls for a probe after exposing the extent of the use of such numbers. His research found the high-cost lines account for 61% of all telephone lines at 16 government departments and agencies.
Calls to 084- numbers cost up to 41p per minute and the Department for Transport earned £2.5 million from calls in two years.
The Home Office topped the list, with 96% of its lines being high cost: 22 out of 23 lines.
The Department for Work and Pensions was singled out for criticism given the number of low-income users likely to use its phone lines.
Services charging 0845 rates include sections dealing with disability living allowance, carers allowance, job centres and the social fund (can provide help for people on low incomes who are facing emergency expenses), as well as at the Pension Service, Insolvency Service, Rural Payments Agency and the Skills Funding Agency (houses the National Apprenticeship Service and is tasked with increasing apprenticeships).
The HMRC also pocketed £4.7 million worth of free services offered by Cable & Wireless in exchange for 400 million minutes of calls to 0845 numbers.
A Driver and Vehicle Licensing Agency spokesman said: "All the DVLA's phone lines for services to motorists are either free or charged at the local rate. Premium rate lines are only in place in response to requests from the motoring industry and any revenue raised is used to offset the cost of providing this service."
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