Sorry to hear about your father-in-law. 
The idea of deferring sounds simplest. Unless you'd made special arrangements for your son to start school a year later than usual, he won't reach compulsory school age until January at the earliest. You have the absolute right to defer his start, so you don't have to get anyone's permission. You just need to inform them.
If the school in oversubscribed and you don't want to risk losing your son's school place, he must start by the time he reaches compulsory school age or by the start of summer term, whichever is earlier. You can still keep him out of school after he reaches compulsory school age, by home educating, but then he may not be able to go to the same school. If you are thinking about delaying his school start that long, you can check whether the class is oversubscribed and whether there is a waiting list in order to help you decide.
At the age of five and six, my daughter spent a great deal of time with her grandmother when she was dying abroad. Though it was hard in some ways, on balance it was definitely the best thing for her to do. I don't think we acknowledge death properly in our culture, especially where children are concerned. Death is an important part of life. Besides, the alternative was for my daughter to be separated from me completely for several months at this difficult time, while I was with my mum, and she would have found that really traumatic.