Association submitted written evidence to the Committee's inquiry on superfast broadband stating that the Government should provide a Universal Service Obligation of at least two Megabits per second (Mbps) in rural areas to close the widening digital divide.
CLA Deputy President Henry Robinson said: "Although hundreds of millions of pounds is being poured into building a better broadband network, rural areas are largely ignored by the major telecoms companies which compete to roll out faster speeds to areas that already have a good service.
"Recognition by the Lords Committee that access is more important than speed is extremely welcome."
Mr Robinson said the CLA shared the Committee's concerns about Broadband Delivery UK (BDUK) and its process for rolling out broadband infrastructure to rural areas.
He said: "With only two out of the nine bidders for local authorities to choose from, BDUK has a flawed procurement process. The concerns raised by the Lords, coupled with those already expressed by the CLA, should force the Government to intervene."
Mr Robinson added that the CLA did not agree with the Lords' recommendation that using fibre optic is the best approach for delivering broadband infrastructure.
He said: "The CLA advocates a patchwork quilt model that uses the most appropriate technologies for a certain area, rather than using a single technology. An over-reliance on a single model is limiting the Government's chance of meeting its 2015 deadlines to provide superfast broadband of at least 24 Mbps for 90 percent of premises, and its commitment to deliver two Mbps to all rural areas."
Read "Broadband for all – an alternative vision" the House of Lords Select Committee on Communications 1st Report of Session 2012-13.