It was agreed to carry out an appraisal of the site to consider potential options for the site, particularly to find out if there is any alternative to demolition.
The total cost of buying the building will be just over £455,000 and will be met by an allocation from the UK government’s shared prosperity fund, not from the council’s budget.
Unlike other buildings in the city centre, 166-168 Commercial Street is not listed and has no architectural merit.
Councillor James Clarke, cabinet member for regeneration and economic growth, said: “One of the key priorities of the city centre place making plan was to tackle empty stores wherever possible to help stimulate the regeneration of the city centre.
“By taking advantage of an opportunity to purchase this block, we can then look at the best way to use the site in the future that will bring benefits to that area. At the moment, these rather ugly buildings are an eyesore and are only likely to deteriorate further.
“They do not meet current demand for retail because of their size and one unit has been vacant for a considerable time. A significant amount of work would be required to bring them up to modern standards.
“We are not closing our minds to any alternative use but, at the moment, it appears demolition would be the best option so the space could be used in a new way.”
