Dunton is working with subcontractor S Fallon and Sons to break up the car park site at North Place to pave the way for a 60,000 sq ft supermarket and five-storey car park.
The project forms part of a wider £60m scheme consisting of sites at North Place and Portland Street, where developer Augur Buchler also secured planning to include 143 homes, a public plaza and bus station.
Housing plots on both sites were sold to Home by Skanska at the beginning of the year. But the planned residential elements were put on hold when Skanska decided to pull out of the house building market earlier this year.
The residential blocks are presently on hold while Skanska seeks a buyer for its sites.