you will have to collect your luggage at SIN - clear customs and then check in again at T1 departures for your onward budget airline flight to Malaya
3 hours should be fine but if your flight from LHR is delayed and you miss your onward flight then you will likely have no recourse with either airline - you will just have to buy another ticket
the airline from LHR may take pity on you and assist but i very much doubt it - am sure you will be OK though with 3 hours