When construction began in March 2022, the budget was just under £34m and the project was expected to be completed by the end of 2023.
WBC said energy prices, manpower shortages, and construction issues all led to the cost increasing.
By July 2025, the cost had increased to more than £46m.
A report to be considered by WBC next week will recommend the budget increase by more than £2.4m to cover all costs, bringing the total to almost £48.95m
In a statement, the council said it would “continue to consider all legal remedies available to seek recovery of costs”.
It added: “The joint strategic committee will be asked next week to allow officers to appoint any additional legal or consultancy firms deemed necessary to complete the WICC and recover costs incurred.”
In a statement, Galliford Try said: “We continue to work with WBC to bring the building back under their control as soon as possible.”