I did this many years ago, when planes were less crowded and it wasn't too bad as we had spare seats around. These days you just can't rely on that.
My daughter has travelled several times with her son and last time stayed overnight at Singapore Airport. This broke the travelling exhaustion and gave them both a good night's sleep before catching the lunchtime flight to LHR the next day. If you can't afford a seat for your son, this is a cheaper option.
Also, make sure you order a child's meal. Last time she had only the option of a baby meal or adult, as she wrongly assumed she would get the appropriate meal automatically.