Whilst the plane will be refuelled, you may very well end up changing planes, depending on your booking. For example, BA has the following regular flights:

LHR-BKK
BA009
depart 22:00
arrive 15:15

BKK-SYD
BA009
depart 18:10
arrive 07:05

LHR-SIN
BA011 BA015
depart 20:30 depart 21:15
arrive 16:10 arrive 17:10

SIN-SYD
BA015
depart 19:45
arrive 06:15

From what you posted above, you appear to be on BA015, arriving in Singapore at 17:10 and flying out at 19:45, the shortest connection. You may be on the same plane you came in on, or you may not, depending on what fleet rotation plans BA has. In any case, it shouldn't matter to you as you are getting off the plane anyways. This is probably the connection I would do, which gives you just enough time to freshen up in Singapore.