Trade union Unison has announced that Kirklees Council staff at two customer service centres at risk of closure are being balloted for strike action.
The council has proposed shutting the two sites, in Huddersfield and Dewsbury, as part of a bid to tackle a budget shortfall of around £20m.
More than 40 jobs would be lost and the most vulnerable residents, who rely most on council services, would be hit hardest by the cuts, according to Unison.
The council plans for customer services to be provided by library staff, but Unison warned that most libraries do not have capacity to take on the extra responsibilities.
A Unison petition opposing the cuts, which has almost 3,000 signatures, has been backed by some councillors, including those on the Kirklees Community Independent Councillors group.
The leader of the independent group, Jo Lawson, said: ‘Vital access to council services will be lost if the two departments close, along with highly trained staff.’
The council said its plan for 10 libraries to offer customer services online and by phone would mean customers could still access the support they needed.
A spokesperson added: ‘The council is going through the necessary HR processes in consultation with unions and affected staff with the intention of minimising the impact on employees where possible by managing vacant posts and supporting staff to move into other roles within the council.’