I understand that if both flights on the same booking reference, luggage can be booked straight through to final destination. If two booking references, luggage needs to be reclaimed and enter the country only to checkin for next flight .
London Amsterdam Amsterdam Dubai last week. Flight to Dubai delayed two hours, the 72 hours was exhausted by one hour. Refused boarding along with half the passenger booked on same flight.
But if your second flight is delayed you will not be allowed to board if even if only outside 72 / 48 hours by an hour, and will to just go back !!! Beware!
I understand that you have to have the flight into and out of Singapore on same booking. I don't think you can arrive in the evening from UK, and fly to Phuket the next morning as many from UK would, staying at airport hotel. Please correct me if I'm wrong.