I don't think it's down to the 'regional' aspect, it's more due to supply and competition.
LHR is one of, if not THE most competitive long haul airport in the world so therefore SQ has be far more price competitive however good their hard/soft products are. Less supply=higher fares. Ask SRB...
With that logic fares at Heathrow are low and airlines are paying mentally high prices to offer basement fares? It's not that simple of course, the front end are cross-subsidising the back end and there's more front end in London remember. This is part of the reason regional direct flying is more expensive in economy.