To be blunt, all buggery will erupt.
None of William's sons is at this stage old enough to hold onto the kingdom effectively; Robert, the oldest, is still a teenager; Henry will never even be born.
The Saxon aristocratic remnant is still active at this stage (Morcar et al made their stand the following year IIRC) then you have the Danes, the Normans barons, Harold's sons etc.
I suspect it would be an earlier Anarchy, on steroids. Your guess is as good as mine as to who would come out on top. My feeling is that the Normans are probably too established even at this stage to be pushed out wholesale, but you never know.