Nigel Paine, the council's director, said he "bitterly regretted" the decision. "We have to focus on the future and make decisions for the benefit of all our customers and staff," Mr Paine said.
Some projects have come to an end and staff will not be redeployed. The three-strong design team has also been made redundant.
The company, which has a turnover of Pounds 4 million and a staff of 110, needed a "different skills mix" to cope with "an incredibly fast-moving industry", Mr Paine said. Council reorganisation had also played a part.