Late payment could be treated as a breach of contract but I believe that it has to be the essence of the contract. The essence must be that getting piad on time is completely essential, and is critical to the work you have agreed to undertake when you signed the contract.
Does this apply to nec3? In nec3 you do have the right to interest on late payments clause 51.2. and termination if a payment due has not been paid within 11 weeks.
The point I think you are raising is that the late payment is stopping the work proceding because you are reliant on the payments to progress the works? Not sure that late payment would be considered a material breach of contract. Will be interested to see other comments on this point.