What if the contract says nothing about final accounts?

You still have one, because the ordinary payment rules, the Construction Act and the contract's own valuation clauses do the work instead. A final account is not a special legal creature: it is simply the last valuation of the works, so on any construction contract the everyday payment machinery carries it. That machinery, from the Housing Grants, Construction and Regeneration Act 1996 (the Construction Act), works like this: you make an application for the closing balance you say is due, the payer must issue a Payment Notice saying what it will pay, and if it wants to pay less it must serve a Pay Less Notice by a deadline; if it serves neither, the amount you applied for generally becomes the sum that legally must be paid. Behind all that sits adjudication, the fast 28 day dispute process every construction contract must offer, which lets an independent adjudicator decide the figure if the assessment is wrong. What you lose when the contract is silent on final accounts is the timetable, not the rights, so set the timetable yourself: submit the account formally, demand a response by a clearly stated date, and if it does not come, escalate on the record through the payment machinery or adjudication rather than letting it drift.

Picture a small electrical contractor working off a one page order that says nothing about how the final account is dealt with. The job finishes and the contractor is owed a closing balance of £32,000. Rather than assume it has no route, it treats the balance as an ordinary payment: on a Monday it sends a formal application for £32,000 and states that a Payment Notice or Pay Less Notice is due within the period the Construction Act reads into the contract. The client stays silent and serves neither. Because no valid notice was given, the sum the contractor applied for generally becomes the amount that must be paid, and if the client still refuses, the contractor can refer it to adjudication and expect a decision ordering payment in about 28 days. The bare order gave the contractor no timetable, so it set one itself, and the statutory payment machinery did the rest.