Can they deduct money without a Pay Less Notice?

Generally no, not from the current cycle. Once the Notified Sum is established, the amount fixed by the Payment Notice or by a valid application in its absence, the Construction Act allows the payer to pay less only by serving a Pay Less Notice, a notice setting out the reduced sum and the basis of its calculation, by the contract's deadline. Set-off, the right to knock one debt off another, and contra charges, backcharges for things like attendance or alleged damage, do not override that machinery: whatever the merits of the deduction, it has to be put through a Pay Less Notice for this cycle or it must wait. If money arrives short with no notice, the shortfall on the Notified Sum is simply a debt, and the usual routes apply: a letter demanding the balance, suspension after proper notice, or a smash and grab adjudication, the fast statutory process that enforces the notice position without arguing the value. The one real exception is a deduction the contract itself builds into the calculation of the sum due, such as retention stated in the payment terms, which is part of the sum rather than a deduction from it.

Say a groundworks subcontractor's Notified Sum for the month is £48,000. On the final date, £41,000 lands with a note saying £7,000 was held back for alleged snagging and a crane standing charge. No Pay Less Notice was ever served. Whatever the merits of those charges, they were not put through the machinery, so the £7,000 is simply unpaid: the subcontractor can demand the balance, warn of suspension, or start a smash and grab adjudication on the notice position alone, and the payer must bring its snagging argument to a later cycle or its own claim. The lesson is that a deduction without a Pay Less Notice is not a deduction at all, it is a debt.