Under the proposals, the building will be refurbished and remodelled to provide 206 new flats as well as new shops on the ground floor and private car parking in the basement.
The application follows the Council's confirmation that it has bid for an exemption from the Government's forthcoming change to permitted development rights, which will allow office to residential conversions without the need for planning permission.
The Council had already indicated in December that it was planning to limit office to residential conversions in the Borough, according to reports in Property Week.
According to the reports, deputy council leader Robert Davis had said that conversions will be curbed as part of the Council's forthcoming city management plan revision.
Davis said the council was considering how to amend its policies to ensure the Borough would retain “an equilibrium” between residential and commercial property. “We are concerned that there has been too much conversion into residential, resulting in a loss to the West End,” he said.