Lots of people have DofE here but it's not essential. I don't have it.... I did do lots of voluntary work and extra-curricular activities, just not in a DofE format.
Oxbridge look at your ability in a subject moreso than any extra activities, IMHO. Of course, if you are able to demonstrate that you can get good grades while still doing extra-curricular stuff, then this indicates you will be able to cope with pace of work at Oxbridge perhaps more than someone who has had to work every minute to get the same grades.