The basic law is this: it IS possible - and not illegal - to bury a loved one in your backyard but you must get the consent of the owner of the freehold of the land.
Kirsty Alsop buried her Mother in her garden in 2014.
Friends of mine have a child's grave in a small wood on their property and have a clause in their deeds that the family can visit once a year. The child died in 1931 and so far, no request.