The number of people signing up to online library services has increased by 600% in some areas since the coronavirus lockdown.
The Local Government Association (LGA) said many councils are seeing a boom in the number of residents using digital library resources.
However, it said that many libraries are restricted in the number of e-books and audio books they can provide because of licensing limits with publishers.
It is calling for the Government and publishers to work together to unlock an additional £5m in investment to enable libraries to increase their capacity in loaning more e-books and audiobooks.
Cllr Gerald Vernon-Jackson, chair of the LGA’s Culture, Tourism and Sport Board, said: ‘Councils are doing everything they can to protect their residents’ wellbeing during this difficult time. Extra funding would help libraries extend their licences and meet this growing demand.’