It was a bit of a surprise when May backed REMAIN as she had been considered to be on the LEAVE side and was even considered as a possible leader of the LEAVE campaign, She was pretty low profile during the campaign itself making only one speech IIRC - clearly positioning herself for a potential leadership challenge in the aftermath every bit as much as BoJo.
Well she got what she wanted although she may (sic) wish that she hadn't now!
https://www.theguardian.com/politics/2015/nov/01/theresa-may-leadership-eu-out-campaign