Civil reg starting in 1837 probably extended the time between death and burial as a death cert had to be given for a burial to commence.
It has never been an absolute legal requirement for a death to be registered before burial/cremation ( although most obviously were).
Although saying that the registrar would confirm the registration to the undertaker, both the 1836 B&D Act and the later 1874 Act had provision for burials that did take place before registration. Such deaths were supposed to be notified to the registrar within 7 days after the burial, with the responsibility on the person conduction the burial. I'm sure in many cases the vicar would tell the family to make sure they did it, but they didn't bother and that probably accounts for some burials being recorded in parish registers that don't seem to have a corresponding death registration.
Funerals still can happen before registration, most commonly in cases where the coroner is involved although a registrar can also issue the necessary permission.
