The elderly and vulnerable will be worst affected if a mobile library is axed, according to critics.
The cabinet wants to save £62,000 a year by stopping the service completely.
It is used by 865 people.
According to cabinet member for culture, recreation and tourism, Geoffrey Bowden it would cost in excess of £120,000 to replace the vehicle.
But after a suggestion from the Labour group he has agreed to consult with voluntary groups to discuss whether they can take on responsibility for the service.
Labour leader Gill Mitchell said: “I really hope this service can be retained because it is absolutely vital for the people who use it.”
Conservative Vanessa Brown said: “I know the Greens say many users of the mobile library also use a static library but it is quite clear that the people who will be worst affected are the elderly and vulnerable.”
According to the budget proposals, 67% of those who use the mobile service also use another library.
Coun Bowden said anyone who is unable to get to another library can access the Home Library Service.
He said: “It is a wonderful service and I would dearly love to keep it but this vehicle is coming to the end of its useful life and at a cost of more than £120,000 to replace it we are left with little choice.”
Under the Greens’ plans the mobile library will initially be parked outside Woodingdean library while that facility is refurbished.
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