Answer: Planning Permission NOT required UNLESS the Permitted Development Rights have been removed - In this case Planning Permission WILL BE required.
You can check your PD Rights by contacting the Local Authority Planning Department.
Where work is proposed to a listed building, listed building consent may be required. The permitted development allowances described apply to houses not flats, maisonettes or other buildings.
Please note: In any event if the garage is to be a habital space it is essential that a Building Regulation Application is submitted to Building Control with details of insulation, floor build-up and other technical requirements.
See photo below of what can be achived when a garage space is converted...
Further info can be found on the Planning Portal
As previously stated, the conversion of a garage, or part of a garage, into habitable space will normally require approval under the Building Regulations.