Payment

I received my first UC payment yesterday 13/6/25 after transitioning from ESA (LCWRA) and Housing Benefit.
This amount is £1248.41 which they say covers the period from 7th May - 6th June.
The payment is what they say I am entitled to for a month.
My last ESA payment was on the 16th May and my last housing payment was on the 8th May.
My housemate pays the rent, bills and council tax from his bank account so I was paying him £115 every week which is my share of that (worked out on a total year cost divided by 52).
Because I couldn't pay him when my old benefits stopped I now have to pay back the arrears plus the ongoing weekly payments until I get my next UC payment in a months time. This totals £805.
Plus I also took money from my savings to live on which I also need to put back.
This leaves me with no money until I get my next UC payment in a months time.
This does not make sense!
Am I meant to get backdated money for the time when I wasn't receiving any ESA or housing benefit?

They are paying £450 for rent.

My last housing benefit was on the 8th of May, which I assume is two weeks in arrears.