It shouldn't be compulsory, but should definitely be an opt-out system instead of the opt-in system currently in place.
I know that there are lots of people who think that registering to vote is a hassle and simply for that reason don't vote. therefore if it were more accessible and enrolment was automatic, I think more people would be inclined to vote.
This opt-out system should be implemented for organ donors as well - anyone who is strongly opposed to it should take the time to revoke their registration. this would mean that the apathetic people who don't particularly care either way would be automatically on the donor list, solving the problems currently being faced by the service.