Opposition councillors last year described the plans as a "Conservative palace to be built in the centre of Dudley"– while the council leadership said the work was long overdue.
The plans to address “long-standing” maintenance problems, increase desk capacity and provide an “improved working environment” at the site were considered by the council in February last year.
In a cabinet meeting earlier that month, Labour group leader Councillor Qadar Zada accused the leadership of having “their priorities wrong” and would be creating a “plush office” while increasing council tax.
But council leader Councillor Patrick Harley said the Grade II-listed building on Priory Road had required "substantial improvement works for many years". He added the council would need to budget for unforeseen problems such as asbestos.
The plans were not approved at full council and were instead passed to the future council scrutiny committee to seek out a way of making the finances for the project work.
A meeting of that committee was held on June 9 and councillors agreed to note the report and endeavour to “identify and make available finances”.
The proposed £4 million cost of the refurbishment is recommended to be covered by prudential borrowing, but debt and maintenance costs would need to be met from the council’s existing law and governance revenue budgets, the report states.
Although the committee moved to undertake the project, final approval of the project and associated finances would need to be considered by the Cabinet and approved by full council.
Papers to council have previously stated the work would include essential repairs to roofs, heating and power as well as refurbishment of office space and toilet areas.
There will also be improvements to the security of door access and the replacement of the Council Chamber microphone system, the papers stated – adding the work would be likely to take around two years.
A report to councillors at a scrutiny meeting said: "The main risk identified recently is around supply and cost of materials required to undertake building works, as a result of Brexit and more recently the lag in supply following the blockage of the Suez Canal.
"Reports generally indicate severe delays in the supply of steelwork, materials required for concrete and external cladding to name but a few. Detailed specification will take into consideration prevailing issues with essential materials and potential substitutions.
"Additionally, not addressing the essential elements of repair will mean there is a risk of disrepair worsening and failing."