MR for LCWRA backdating

Hi there. Is it possible to get some support for a lcwra mandatory reconsideration please? Long story....

I was awarded pip December 2019 after waiting from February 2019 for an assessment. I told pip in December that I had been awarded pip and updated the health section. I received a reply saying no need to do anything on UC. I was unaware lcwra etc existed. As I also have a disabled child, I was at that point not required to look for work, so not fit note would have been necessary for me to be put in any non work group. Fast forward to September when I move house and because of my health needs I've always had adult social services assistance. My new coi cjl spotted right away I didn't have lcwra on my claim and I went straight to uc and raised a complaint. They asked me to get a fit note backdated to the previous December (which my gp happily did) and they'd look to backdate it. I had my assessment two days ago and was awarded lcwra today. I was barely on the phone 15 mins and she said she had all she needed to conclude the assessment. But on asking uc today I've been told the claim has only been awarded from October when I actually uploaded the fit note. They said I can do an Mr, which I explained why I wanted one. I don't feel I should be penalised because my son is also disabled. And I did tell uc at the time and they ever asked for anything, literally replied saying I need to do nothing. What are my chances here? This is an awful lot of money and I absolutely believe there is evidence I did everything appropriately.

Thank you

Just to add to this I did raise a complaint in October and the letter I have states it was not dealt with correctly.

As this stand I submitted my fit note on 23rd October 2020, assessment period is 8th to 7th, payment date 14th. Uc have said payment would be made if Mr not dealt with or successful from Feb. I made it March?

If Mr is successful fit note is from 31st December 2019, same assessment dates. So when would payment have been from then? Would it be may?
Thank you

Sorry I realised I wrote pip twice! I mean when I was awarded pip I updated my uc by writing in my journal and filling out the health section in changes. That was 31st December 2019. In normal circumstances they would have asked me to provide evidence, they didn't. I raised a complaint in October 2020 where I received a written response saying it had not been dealt with by uc correctly and a UC50 form was sent out and I then submitted a fit note backdated to 31st December 2019. I have since had a wra assessment and was awarded lcwra. From October. I have asked for an Mr due to their mishandling of my health info back in December 2019. Does that make sense? I told them I was not fit for work and they did nothing and told me that was all I needed to do.

How do I work out when payment would be due?