The first thing to happen is that the LA will write to inform you that they intend to obtain a liability order in the Magistrates’ Court, which you do not need to attend unless you are not the person they claim is liable to pay business rates, when they have obtained the liability order and it is rather just a rubber stamping exercise, they will then send the debt to a debt collection agency/bailiffs to recover the debt.
The VOA should not take long to determine the correctness of your claim, so do as BM suggests and pay your business rates until they reach a decision, a refund may be due.