Ministers have been urged to reaffirm their commitment to offering a national minimum broadband speed.
The government has promised to give everybody the legal right to request a broadband connection capable of delivering a minimum speed of 10Mbps by 2020.
However, the Local Government Association (LGA) pointed out that with with recent ministerial changes and delays to the government's digital strategy, a timetable of action is now required.
The LGA also insisted that while the proposed 10Mbps is a "good start", it must keep pace with national average speeds and the expectations of households.
Councillor Mark Hawthorne, Chairman of the LGA's People and Places Board, commented: "Without this there is the real possibility of some areas - particularly in rural and hard-to-reach areas - falling into a digital twilight zone.
"Achieving 10Mbps should just be the start and something to build on because demand for and availability of faster speeds continues to grow. "
Cllr Hawthorne also insisted that good digital connectivity is a "vital element" of everyday life in the 21st century.
Indeed, he said it is "undeniable" that access to a fast and reliable broadband service is a necessity for homes and business across the country.
Cllr Hawthorne went on to state that local authorities are ideally placed to understand the digital needs of local areas.
He said councils have been at the heart of improving digital connectivity, as they have organised initiatives to equip residents and businesses with digital skills, worked with mobile operators to best place infrastructure and helped implement superfast broadband programmes.
LGA figures show that about £740 million of the £1.7 billion invested in improving digital connectivity via the Superfast Broadband Programme has come from the local government sector.
"Ensuring residents and businesses across the country are provided with fast and reliable digital connectivity will be key to achieving the government's ambition of an economy that works for all," Cllr Hawthorne added.