Northampton Borough Council is in dispute with trade union GMB over proposals to make one of the three Guildhall security officers redundant.
A union member said the council wants to make the redundancy by April 1.
In the meantime, the authority will continue to plan the installation of an extra security door for the One Stop Shop, which is likely to be completed after April.
A spokesman for the borough council said it was not appropriate for the authority to comment on employment matters.
But David Day, membership development officer for GMB, said: "I'm unhappy with the process. Not enough questions have been answered.
"It's a shame we've got to this point but hopefully we can find a resolution.
"The remaining officers are going to be overworked and financially worse off. It's not a thought-out policy."
A meeting has been scheduled for February.
The leader of the borough council Labour group, Castle ward councillor Danielle Stone, wants the full security team retained as it is because it runs the guided tours of the Guildhall as well as helping to run events there.
“I am sad to find that the GMB is in official dispute with the borough council over its plan to restructure the Guildhall office team," said Cllr Stone.
“The dispute has come about over council failure to consult the union on the restructure.
“In my view, good employers benefit from having a unionised workforce in many, many ways. The unions support staff.
“They act as the voice of the staff in negotiations with the employer. They keep staff well-informed of what is going on. They support and ease change management at work. They also offer training to staff.
“It is in the interests of employers to work well with the unions.
“I urge Northampton Borough Council to get round the table with the unions and sort this matter out, quickly, simply and for the benefit of all.”