Got refused back dated severe disability premium

Hi, i found out through a benefit checker i should of been getting SDP. I applied and they have awarded it me but in the letter didn't mention anything about back dating it to when i should of been entitled. I phoned them and they said because i didn't notify them my son had moved out at the time then they can't back date it. i suffer with mental health and honestly thought i had but they said they have no record so its possible i might of missed them. Is it right that it cannot be back dated? On a previous phone call when i filled in the form the lady said they had ways of checking anyway.

To help people in the future I want to share the conclusion to my previous post.

I found evidence that I did actually inform them that my son moved out but the date I sent it was two weeks earlier than I thought it was. This is why they claim I couldn’t prove it, because there was nothing from the date I was saying. Why they wouldn’t have looked back a little further when I was expressing how sure I was I had told them I don’t know. The sceptical part of me thinks they were hoping I would just accept it. However once I had the date and could prove it they found it straight away and had to award me.

Moral of the story ALWAYS keep your own evidence. Mine in this case was I had taken a photo of the letter before I posted it