NEC ECC: Are there any occasions when you can refuse to act on an instruction?

Yes. If the instruction is not one in the contract or is an instruction to do something outside the scope of the ‘works’ description.

A Contractor is required to obey an instruction given by the Project Manager or the Supervisor, with the proviso that it is instructed ‘in accordance with (the) contract’ (clause 27.3).

If in doubt, you could always ask the Project Manager or the Supervisor to state which clause they are instructing you under, so you may decide whether they are acting within their contractual authority.

Directly answering your question, an obvious example would be where you are instructed to undertake an illegal or impossible requirement, or where the instruction possibly conflicts with an obligation under the contract or a statutory requirement.