delay in decision to end award leading to gap in entitlement

UC assessment period runs from the 2nd of the month, to the 1st of the following month.

In August, client received two wages due to 4-weekly wage payments pattern, which would be enough to remove entitlement for that month. The normal earnings received during September would be low enough for UC to be awarded again.

The decision about the August double-wage was apparently posted to the client’s journal on 1st October, and the claim closed. We might have expected this decision to normally have been made on the 8th of September, JCP said the delay was likely because it had to go to a decision-maker.

The decision finally made on 1st October apparently didn’t include any assessment of the 2nd September to 1st October assessment period. I haven’t actually seen the decision, as that journal is now inaccessible, due to the client making a new claim UC on 2nd October.

Client therefore has a gap, having received no UC for September. Even had one been attempted, I guess that no new claim would have been possible during September, given that a UC claim was already “open”?

My initial thought was backdating on the new claim made in October, though not obvious which criteria for that applies here.

Is there any argument that the decision posted on 1st October might have been capable of including entitlement for the 2nd Sept - 1st Oct period, or was the decision made a day too early for that to happen?

Is there any other recourse for a delay in decision-making leading to a gap in benefit entitlement, apart from a complaint?