Mansionhouse Road does not have any other newly-built houses or structures visible from the street. A new two-storey house squashed in between historic buildings, and next to a B-listed building, would seem rather out of place and certainly ruin the historic feel of the area.
By all means, go ahead if wanting to ruin the beauty of the street; as this new structure would, in simple terms, look ugly.
The solution would be to build the new house in a sympathetic style to the original building next door, and one storey so that it would be less visible from the street.