The closure of four public libraries as part of a drive to save North East Lincolnshire Council £5m will go ahead.
The authority has warned a further £10m may have to be saved
It comes despite strong opposition from residents who presented a petition to one of the council's watchdog scrutiny committees on Thursday.
Nearly 3,000 residents signed the petition against shutting libraries on the Willows, Yarburgh and Nunsthorpe estates and Scartho library in Grimsby.
The committee has noted the petitions, but the libraries will shut in October.
The closure plan follows an announcement in August that the authority was to make major cuts to public services, along with the loss of 20 jobs.
The authority needs to meet a shortfall of £5m in its budget and has warned £10m will also have to be saved.
Almost all public toilets in the area are also set to close.
Other cuts are in social services and education, and motorists can expect an increase in car parking charges.