Ministers should introduce a social tariff to ensure the poorest people in society can get a good broadband connection, councils believe.
The government has pledged to implement a new broadband Universal Service Obligation (USO) that ensures everyone in Britain has a legal right to request minimum speeds of 10Mbps by 2020.
According to the Local Government Association (LGA), the USO should ensure that those who might face "undue hardship in paying a market rate" still get adequate connectivity.
The organisation believes this is vital since government services are increasingly switching to digital, while online access is considered an essential safety net in current social and economic conditions.
Furthermore, it said broadband access can help to reduce social isolation, as well as enable people to be cared for outside hospitals more easily.
The LGA stated that since BT already allows qualifying customers to receive a basic subsidised telephony and broadband package, suppliers that deliver the USO should provide a similar offer.
Councillor Mark Hawthorne, Chairman of the People and Places Board at the LGA, commented: "Good digital connectivity is a vital element of everyday life for residents and can help them cut household bills, shop online for cheaper goods, stay in touch with distant relatives, access their bank accounts and even run their own businesses.
"As central and local government services become more digital, the USO will need to provide faster and more reliable speeds and, for our most vulnerable residents, a subsided connection at an affordable price."
Cllr Hawthorne pointed out that the quality of digital connectivity can vary significantly from area to area, with some communities able to access superfast broadband speeds and others achieving "substantially less".
"Councils want to see a social tariff enabling all people to be able to access a subsidised broadband service," he added.