If your garage conversion falls within the ambit of permitted development (pd), you may not require planning consent in London. 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. In London you would also require formal approval to alter the use of a detached garage.
It is possible that your pd rights may be revoked, however it is still possible for you to ask for approval from householder planning by putting together any design sketches and approaching them for the requisite permissions. That would cost £500, plus any design fees. 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 You may also be required to apply for listed building consents or party wall agreements to complete your conversion.