Can I suspend work for non-payment?

Yes. If the sum due has not been paid in full by the Final Date For Payment, the last day the money can lawfully arrive, and no valid Pay Less Notice, the notice that cuts a payment down, reduced it, the Construction Act gives you the right to suspend, meaning to stop, some or all of your work until you are paid. The right only arises after you give written notice of at least 7 days saying you intend to suspend and on what ground, and it lasts until the money owed is paid; once you have properly suspended, the Act also lets you recover the reasonable extra costs the suspension causes and claim an appropriate extension of time, more days to finish. Suspending without that notice, or over a sum that was never actually due, risks being a breach of contract by you, so check the paper trail and the exact contract wording before you down tools.

A plastering subcontractor is owed a Notified Sum of £40,000 with a Final Date For Payment of Friday the 30th, and no Pay Less Notice was ever served. When the 30th passes with nothing paid, it does not just walk off site. It sends written notice saying that if the £40,000 is not paid it intends to suspend work from at least 7 days later, say the 8th, and on what ground. If payment still does not arrive, it can lawfully stop, stay off until paid, and later recover its reasonable extra costs of stopping and restarting plus more time to finish. Had it downed tools immediately with no 7 day notice, or over a sum a valid Pay Less Notice had properly reduced, it would risk being the one in breach.