The decision was signed off by planning officers on Friday 22 May under delegated powers.
The scheme will see the vacant supermarket converted into 12 flats, with two retail units retained on the ground floor.
Wroughton and Wichelstowe Parish Council has criticised the approval, arguing the development does not provide enough parking and could add to congestion along the High Street.
According to the parish council, the plans are nine parking spaces short of the minimum requirement for a scheme of that size.
Councillor Holly Woodward, chair of the parish council’s planning committee, said councillors were “really disappointed” by the outcome, particularly as the borough council’s highways officer had recommended refusal.
She said:
“While we would of course like to see the former Co-op building put to use, it’s no good approving plans that could exacerbate the car parking problems on the High Street.
“It’s really important that the parish council stands up for local residents, many of whom were clear that on the subject of car parking, this planning application falls short.”
Residents living on the High Street raised concerns at a parish council meeting earlier this month, warning that parking in the area is already under pressure.
The application was not determined by elected councillors at a planning committee. Instead, it was decided by officers using delegated powers.
Thomas Haworth, deputy clerk at the parish council, said most applications are handled in this way.
Mr Haworth confirmed the parish council does not intend to appeal to the Planning Inspectorate and does not expect the chair of the borough council’s planning committee to intervene.
The approval is expected to divide opinion in Wroughton, with some welcoming the reuse of a long-vacant site and others questioning whether existing parking pressures have been fully addressed.
