One of the topics I haven't seen discussed is what will happen after the connection goes off BUT the airlines have already given you the boarding pass(es) on the onward connecting flight. I suspect that this is where airline status of the passenger comes in to play. Comments serfty? I can't see the airlines not assisting where the BP has already been issued. If the OP's flight from LHR is delayed sufficiently (ie the departure), the danger is the connecting BP won't be issued.

Having said that I have connected in SIN on separate tickets many times - but almost always from an Asian connecting flight (CX/JL) and allowing a minimum of 2.5 hours (or more). And ideally an alternative initial flight as a possibility.

Happy wandering (if possible)

Fred