BrE uses both. You will hear "He keeps to himself", "He keeps himself to himself" and even "He keeps very much to himself".
The most common use (unfortunately) of "He kept himself to himself" is when neighbours are interviewed about someone who has done something terrible (a murder, a terrorist attack etc). News reporters quite frequently interview the person's neighbours to find out some background. Generally, if that person has done nothing to draw attention to himself, lived a quiet life with no reason for his neighbours to have paid much attention to him, they'll tell the reporters things like "He was a pretty quiet guy - kept himself to himself. I can't believe what I'm hearing about what he's done!" (Needless to say, this doesn't apply only to men!)
Student or Learner