If there's no change, the T3 is used for both flights. However, you can't remain on board as you suggested because this is not routine in SIN, and DPS & LHR are operated by different airplanes - B787 and A380, respectively.
It's a big terminal, and based on my experience there (but not recently and to the same destination) if your flights are on time, even though the 2 gates can be far apart from each other, you can get to the departure gate within that time frame on foot and using travellators or by train service that connects some gates.