The report states that the rural broadband programme will deliver results 22 months late and confirms the CLA's long held view that the original deadline of May 2015 was unrealistic.
CLA President Harry Cotterell said: "For the past two years we have said there is no conceivable way 2015 targets would be met by rolling out superfast broadband through Broadband Delivery UK and Local Authorities.
"What really concerns me is the lack of transparency in the procurement process. With BT the only bidder, the lack of competition brings into question the programme's value for money."
Under the rural broadband programme, the superfast network should be accessible by 90 percent of the population by May 2015.
However, the NAO report has said that only 9 out of 44 local projects will be able to meet that deadline.
Mr Cotterell added: "To have so few projects likely to complete by May 2015 is a shocking indictment of the way this has been carried out."
The CLA President is writing to Culture Secretary Maria Miller to request clarification of concerns that the Government's other objective - ensuring there is access for all to at least two megabits per second (Mbps) by 2015 - may also be delayed to 2017