I was told during my IMCr training that an approach can be logged as instrument, if it is carried out by "sole reference to the instruments" -
I'd very much like to see a reference for that. Anyway, who can tell what the pilot was doing in the cockpit? He might have flown the approach autopilot-coupled, while reading Stick and Rudder
so I would always log an ILS as an instrument approach - even if it was in VMC.
This debate, in both UK CAA and US FAA terms, has been played out in every pilot forum (UK and USA) going, and must be a close second in terms of forum server CPU loading to old favourites like foreign VMC on top on the IMCR
There simply is no legislation on this, and legally that's the end of it.
Morally, it's up to you. I think most pilots will log an IAP only if a part of it was in actual IMC, or there was IMC around so one would expect to encounter some on the way in.
A more strict approach (no pun intended) is to log it only if you are in IMC at the FAF.
A more strict approach still is to log it only if you fly it on instruments down to the minima. This would imply that some 99% of the time you would need foggles and a safety pilot OR you fly it solo but the weather is so bad that you go missed and you actually land elsewhere (which is dangerous because deliberately flying to places where you know you will go missed will eventually bite you on the alternate as well, because stuff like OVC001 tends to be widespread). So IMHO this interpretation is silly.
The FAA has issued various rulings over the years but they have changed them so many times.
Personally, I would not log an IAP if it was obvious from the METARs that the conditions were clearly VMC - unless flying with a safety pilot and then I get consent to use his name in the logbook as per the rules