Generally there does not seem to be a definite reason as to why there are no funerals on a Sunday unless the deceased is of the Muslim or Jewish religion. There are no laws that can be found against it.
It can only come down to three valid reasons. One being that the churches are too busy conducting services for their congregations. Secondly it’s a day of rest in most cultures. Thirdly, to have staff work on a Sunday to take care of all things related to a funeral would cost too much.
As with tradition in a lot of religious homes many go to church for the morning service. Most return home for a Sunday lunch with family and do their own thing for the rest of the day. After services have been completed it’s only fair that the vicar or pastor (depending on the religion) is entitled to a rest as well. He does attend to all church matters such as weddings, funerals, baptisms and all the other church matters during the week.
The majority of companies, except the retail industry and emergency services close for a Sunday. And supposedly many don’t want to attend funerals on a Sunday. It would appear to be an unwritten rule amongst the majority.
Cost of having funerals on a Sunday is another factor in terms of labour. Everything can be sorted and paid for during the week, but it’s the actual act of the funeral that would cost. There are a number of people involved to help make a funeral happen. The undertakers, priest right down to the gate keeper are all people that need to be paid to be there. With labour regulations people are paid more for working on a weekend, with Sundays being the highest paid day of all. This would considerably add to the cost of a funeral to be held on a Sunday.
If you wish to have a funeral on a Sunday there’s no one stopping you but be prepared to pay more than for one to be held during the week.