guys, a bit off-topic question but relevant for KUL-SIN tread: what is the reasonable/minumum transfer time between flights in Changi airport?

I will be landing in SIN at 19:45 (SQ from KUL into Term2) and will need to catch up flight departing at 22:40 (BA from Term2).

Is 3 hours emough to disembark, take luggage, transfer, check-in, some shopping and drinks/shower in the BA departure lounge?
Or do I need to take a previous KUL-SIN flight arriving at 17:45?

Will I have to go through Singapore immigrations (arriving from KUL and departing to LHR)? How long it might take on a Sunday night?

many thanks for recommendation/advise

mishkira