Okay, here's some more info on my problem.
I noticed I was getting this error, which I'd been foolishly ignoring!

I traced this to HFSLIPWU.INF somewhere around here
CODE
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","214",0,"%11%\regsvr32 /s """%11%\wuaueng.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","215",0,"%11%\regsvr32 /s """%11%\wups.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","216",0,"%11%\regsvr32 /s """%11%\wups2.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","217",0,"%11%\regsvr32 /s """%11%\wuweb.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","218",0,"%11%\regsvr32 /s """%11%\wuapi.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","219",0,"%11%\regsvr32 /s """%11%\wuaueng1.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","220",0,"%11%\regsvr32 /s """%11%\wucltui.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","221",0,"%11%\regsvr32 /s """%11%\iuctl.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","222",0,"%11%\regsvr32 /s """%11%\muweb.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","223",0,"%11%\regsvr32 /s """%11%\msxml4.dll""""
HKLM,"SOFTWARE\Microsoft\Windows\CurrentVersion\RunOnceEx\ZZB","224",0,"%11%\regsvr32 /s """%11%\msxml6.dll""""
I loaded up services.msc to once again find no Automatic Updates service. Then I ran the first command from the section I've just posted,
(obviously without the unneeded switch, multiple quotes or path)CODE
rundll32 wuaueng.dll
After a refresh in services.msc the service was now shown.
I ran Windows Update but it failed to work!
When I checked again in services.msc, the service needed starting.
However, when I tried that I got this!

A reboot later and 'all was fine', the service started and WU ran fine.
As a final addition to my woes, WU reported that I needed these
CODE
KB898461
KB892130
IE7
KB918899
KB885836
The second and third are understandable, however the other three are already in my HF folder!
Here they shown in Add or Remove Programs minus IE7 as proof.