Civil Aviation Authority (CAA) and SMS - no health included. CAA SMS doesn't consider Health, because the Health and Safety at Work Act adequately covers it. For that matter, SMS doesn't cover a lot of what he HSaW covers; it isn't concerned with what happens on a day-to-day basis, that doesn't cover aviation risks. Although there is a lot of overlap with the HSaW, in that there is enough commonality in methodology, the focus of the SMS is Aviation Safety, and really outwardly focussed, while HSaW is inwardly focussed.
I's be interested to hear who you have been dealing with, as at the recent CAA SMS forum, it was made very clear that a company's SMS should be their manual and system, and preferably combined with the H&S policies. I'd stand your ground with that issue. CAA are a very different regulator to Worksafe - they are (in my experience) are a lot more open to different ways of complying.
P.S. if they're charging for you to talk to them, then you're talking to the wrong group. The SMS team generally aren't charged out.
Happy to talk off-forum if you want to discuss specifics.