Do I have to accept their final account assessment?

No. Their assessment is just one side's opinion of what the account is worth, and unless a conclusive evidence clause (a term that makes a certificate or assessment binding once a deadline passes) has already hardened it into something fixed, you are free to challenge it. Respond in a set order. First check the machinery: work out whether any final certificate or deadline is about to make the assessment conclusive, because that decides how much time you have. Then demand the reasoning line by line, because a figure valued at nil with no build-up is usually far weaker than it looks and often cannot be defended when tested. Then concentrate your challenge on the heads that carry the real money rather than fighting every line at once, which wastes effort on figures that will not move the outcome. Adjudication, the fast 28 day process an independent adjudicator uses to decide construction disputes, is available at any time, so if talks stall, referring just the single largest disputed head is often what breaks the deadlock and repositions the whole negotiation.

Say a joinery subcontractor submits a final account of £120,000 and the main contractor's assessment comes back at £70,000. The subcontractor first checks whether any certificate or deadline is about to make that £70,000 binding, and finds none, so its rights are still open. It then asks for the build-up behind the assessment and sees the biggest gap is a family of variations the contractor has simply valued at nil, with no reasoning attached. Rather than fight all fifty lines, the subcontractor concentrates on that variation head, worth £35,000, where a nil with no explanation looks weakest. When negotiation stalls, it refers just that head to adjudication. An adjudicator's decision that the variations are worth, say, £30,000 does not only recover that sum; it tells both sides how the rest of the account is likely to be viewed, and the remaining figures usually settle quickly around it.