Do i have grounds to claim for a HB underpayment from lat July?

so on 9/7/18 i moved property that was only one mile away but as it crossed an invisible border i was now under a new council
i contacted my previous council informing them i was moving address around 2 weeks before moving out

as the town remained the same on my address i was oblivious of this change of councils until i received a generic letter rom the new council addressed to 'the occupier' about a council tax bill, a month after moving in

so i then went through the process of applying for my benefits (HB + ESA) with the new council, which after having my application/evidence returned was told i now apply for UC, which i done

However, upon checking, the 1st council had stopped paying me HB from 28/6/18 and after asking they said because they apparently wrote to me but i didnt reply - i never received any letter like this before moving out

so these 11 days before moving out without housing benefit meant me losing £333
i know its been 9 months since i left the previous council but do i have any grounds to get these unpaid monies?

if it was the other way around and they learnt they overpaid me £333, 9 months later, im certain the council would enforce repayment