This trial is designed to evaluate the safety and effectiveness of transplanting retinal pigment epithelial cells (RPE) in patients with Stargardt's Macular Dystrophy. The trial is being conducted at NHS Lothian Princess Alexandra Eye Pavillion in Edinburgh and Moorefields Eye Hospital NHS Foundation Trust in London, in conjunction with Advanced Cell Technology. Participants will receive different doses of the RPE cells, which have been made from human embryonic stem cells. Participants will be monitored for complications including infection and tumour growth, as well as structural evidence of successful engraftment and changes to vision. The trial expects to enrol 16 subjects by January 2014.