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Seeing as we're being technical...
If there is no bicycle picture, then the markings are not compliant with the TSRGD Schedule 6 1001.2*, so there is no advanced stop line, just markings on a road ahead of the actual stop line.
Meaning that if you cross it on a red light, you are committing an offence.
Of course, if there is a cycle lane, and the first stop line is broken by the cycle lane, then it is not a stop line at all, again just markings on the road.
Meaning that anyone can cross the line at any time, and no offence is committed.
* This stuff gets me so hot
Obviously, it would be the fault of the highway authority (Transport for London) in the first place for applying incorrect markings, but the absence of a bicycle symbol in itself isn't a reason for riders not to be able to use the advanced stop line area.
Both ASL zones that I can see don't have a cycle symbol (on the Chelsea Bridge Road approach, a cycle symbol seems to have been burned off, and on the eastbound Chelsea Embankment approach, there doesn't seem to have been one (just going by StreetView, which may of course be out of date)) have a short length of angled dashed line at the nearside, through which it is lawful for any vehicle that fits to proceed, i.e. pedal cycles and motorcycles, as it is not part of a stop line.
As with any other ASL, if you actually cross the stop line (as opposed to an entrance like the angled dashed lines) at red (which, of course, everybody does all the time), you're technically committing an offence, anyway, and this is never enforced as it would be an impossible nonsense. The PCSOs would have been correct had the stop line been solid all the way along, without the angled line (which should really be applied to the beginning of a full lead-in lane the length of the average car queue, but because TfL usually prefers cramming in more motor traffic stacking lanes rather than cycle lanes, such lead-in lanes are often not provided or not the length of the average car queue).
Hope that was a little clearer than mud. ASLs are a messy idea and basically don't work whichever way you look at them.