This is likely to be called permitted development (pd) so the formal planning consent in Bexley would typically not be necessary. Some modern buildings are subject to restrictive covenants requiring that the garage be maintained as a parking area, which will need to be discharged (check the deeds to find out if this is true). In Bexley you would also require formal approval to alter the use of a detached garage.
Don’t worry that you will not be able to follow a scheme if your pd rights have been revoked, we are on hand to help you put together well thought out sketches to ask for appropriate permission from householder planning. Excluding design fees, the cost for that will be £500. Any major structural changes that will be made throughout the building project, will require a completed householder planning application. Depending upon the property where you wish to carry out the conversion, we may need to apply for various permits, for example if you reside in a listed building, or you have adjacent neighbours.