Fit note renewal new style esa

My fit note runs out tomorrow and I contacted the gp a while ago about extending it. When I chased with them they said the gp won't look at it until it runs out and then if approved they will back date the new one so there are no time gaps. They may not do it tomorrow so technically I could be a few days with nothing on file. They told me the dwp understand that and it shouldn't be a problem. Should I be worried? I am still waiting for my medical assessment. I asked if I could turn down one date offered as it was so far away and they said they could put me on the waiting list for a telephone appointment which is much better for me, but I am still waiting!