I lost my ESA after a reassessment in October. (I won my very first claim for ESA after an appeal in 2011, so this is not a new claim.) I have had my MR rejected, and have just sent off the appeal documents, and a fit note from my doctor backdated to when my ESA ended in October. I am still rather confused whether my assessment ESA will cover the MR period as well as the appeal period. In my case, it took DWP 8 weeks (!!) to deal with my MR, so it's a reasonable amount of money.
Providing you Fit Note covers you from the day after your ESA ended and you claimed no other benefit during the interim then you should receive back payment of the Assessment rate, however, the ESA will not be re-instated automatically, you need to contact the DWP when you and they have received confirmation that your appeal has been accepted by the Tribunal Service.
I assume you sent your Fit Note to the DWP and not the TS.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems
