This is likely to be called permitted development (pd) so the formal planning consent in Hammersmith would typically not be necessary. It may be necessary to discharge any restrictive covenants pertaining to your modern property, such as that the garage be maintained as a parking area. By changing the original use of your detached garage, you may be required in Hammersmith to apply for formal approval.
Our competent construction team may need to assist you in asking for approval from householder planning if by any chance your pd rights have been revoked. The cost would be £500 with any additional design fees as extra. If you want to drastically alter the exterior appearance, such as making major changes to the windows, using new materials, or incorporating an extension, a complete application would also be required If you have adjacent neighbours or you reside in a listed building it could be that you will require listed building consents or party wall agreements to undertake a conversion.