Personal reasons aside, the cost to the airline in terms of dumping fuel, returning to LHR, offloading the deceased, finding and offloading luggage, re-doing paperwork, re-fueling and then getting en-route again (which would all take hours before finding a new slot even comes in to play) is surely something which would have been considered by the pilot too. People will onward connections from SIN would also have to be re-booked at the airlines expense too. That would affect far more people in a bigger way than simply sharing the cabin with a dead body.
If the deceased was Singapore resident then it would make more sense to continue to SIN anyway to save the family big repatriation costs, which on top of a death are not exactly welcome.
There are countless reasons to continue to the intended destination and I think most pilots would have done so.