This is likely to be called permitted development (pd) so the formal planning consent in Islington 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 Islington to apply for formal approval.
By putting together any design sketches and asking for approval from householder planning, you will still be able to convert your garage even if your pd rights have been revoked. The cost would be £500 with any additional design fees as extra. Large structural alterations such as changing windows, or incorporating an extension would require you to complete an 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.