Not 100% sure of the context of your question, but It depends who these “other parties” are, and who they are contracting with. Under the ECC contract the Project Manager and Contractor can raise early warnings to each other. If the Employer has engaged the architect or designer under a PSC then they can raise an early warning to them under that contract under clause 15.1.
If this is an external body that the Project Manager/Employer has no direct contractual link with then by all means they can raise an early warning but it will have no direct contractual standing or any recourse if the receiving party fails to address.