"So, I wasted about an hour of my time signing up to Family History, then found out that the film reference number cannot be viewed! Does anyone know where FH get the film images from?"
As @MikeRafone said, these are the Mormons. They have been collecting family tree stuff for a very long time.
I guess that you went to
https://www.familysearch.org/search/catalog
and clicked on the Film/Fiche/Image Group Number?
This is where you enter the FHL number.
What you do next depends on what it says.
You may be lucky and some of the images are available online. Although, in that case they are also likely to be available online through Ancestry and other sources as well.
To give a specific example, I was looking for number 425436 / 856929
When I looked for these numbers I got a number of different things come up:
https://www.familysearch.org/search/catalog/results?count=20&query=%2Bauthor_id%3A272941
Some of them, in particular the Bishop's transcripts, were available online (for free from FamilySearch but also on Ancestry). But the actual parish registers were not.
What it says that you have to do then to view the images is to go to a FamilySearch Centre or an affiliated library.
You can search for these here. I live not too far from Cambridge so this map is centred on Cambridge. Just change the place.
https://locations.familysearch.org/en/search?qp=Cambridge%2C+Cambridgeshire%2C+England%2C+United+Kingdom&lat=52.203482&lng=0.123582&r=25
If you get in touch with the nearest centre or library you can an make an appointment to view any particular images you want.