Costa Maouidis had applied to demolish 15 and 15a Queen Street, which are currently in use as the Pheasant Grill and a storage unit.
He had proposed to replace it with a "new build incorporating two retail units and two one-bed flats and four two-bed flats".
In his proposal he said he may have decided to use the new retail units to carry on as a cafe or takeaway.
Shropshire Council officers refused the application. A decision notice from planning services manager Ian Kilby said: "The proposed development is located in the conservation area of Market Drayton where there are historic buildings.
"Under the National Planning Policy Framework and policies CS17 and MD13 [of the Shropshire Local Development Framework] a heritage impact assessment must be provided to ensure that the design and scale of the building and any potential archaeology are appropriately assessed.
"The lack of this information is contrary to adopted local and national policies."
It went on: "The size and scale of the proposed development is not in keeping with the scale of development adjacent to the site. In the absence of a heritage impact assessment to justify the scheme, it is considered that the scale of the proposal and its potential design is not acceptable in this historic location."