'gov-notifications.co.uk' is also a domain name that's never been registered. (Any address, genuine or false, can be entered into the 'from' or 'return to' field in an email).
Any genuine email from the NHS would have '.nhs.uk', or possibly '.gov.uk', in the address. (It could also have the address of a third-party provider, such as 'my-healthbook.co.uk', who is acting on behalf on an NHS provider, but it certainly wouldn't show an entirely fake domain name).