You don't call 999 unless there is a chance that the person can be revivied, you just call the GP to certify death if the person has been ill and death expected.
You can keep the body at home if you want to (unless there has to be a post mortem) although it is unusual. You don't have to use an undertaker - you can arrange the burial or cremation yourself and the funeral service (if you want one, you don't have to), buy a coffin and transport the body yourself.
You can bury your loved one in your own garden except in certain circumstances.
The only things you have to do is get the death certificate, signed by one doctor for a burial, two for a cremation; register the death and ensure the body is lawfully buried or cremated.