HSE will usually use the contact email address that was given on the employers details online when the 'Registration' was completed.
I recommend a specific email address is created for this purpose e.g. radiation@... then key people added to this address e.g., RPS, Head of Science, Business Manager etc.
In the case of LA schools that will be the LA, so who do they contact?
If a school changes to an academy now subsequent to registration presumably they have to register again? If a MAT then it will be the admin of the MAT who do that?