As the payment of rent is your contractual responsibility, any rent that is not paid via Housing Benefit is your responsibility. Even if there is a dispute over how much Housing Benefit has been paid (i.e. you think you should have more), until the dispute is resolved you are responsible for the arrears.
The rent arrears pre-action protocol requires that your H/O ensures all HB related situations are resolved before taking serious action against your tenancy. This only applies however where the delay is outside of your control and you have provided all relevant information to your local council and where you have maintained regular payments to your account.