Have to agree with Ready, I find no problem at all with flying a standard speed controlled approach in CAT3 weather. The aeroplane does not fly any different because it's foggy, the delays into LHR are bad enough in LVP's without everyone flying at vref all the way down the ILS.
Any modern jetliner autopilot is quite capable of flying a CAT3 approach while the aircraft slows down and flaps are run out etc. I suspect that the rule some companies have harks back to the days when autopilots were a bit dodgy and not very good at approaches. If the SOP's for a modern aircraft specify a fully stable approach for CAT3's they need to be rewritten to reflect the modern world.