As they do not fall within any of the exceptions where HB can be claimed, they obviously cannot claim HB.
They can claim UC, either under the care leavers provision, or, failing that, I cannot see how a care leaver woud not fall under the catch-all: "You cannot live with your parents because of a serious risk to your physical or mental health or significant risk of harm, or because it is inappropriate for you to live with them for another reason."
https://www.gov.uk/guidance/housing-costs-for-18-to-21-year-olds
It's always fun explaining the DWP's own rules to them. I have had to do this with those on ESA C / JSA C who were told by the jobcentre that they cannot claim UC housing costs, students, and a host of others where the Jobcentre helpfully referred the customer back to us to claim HB.
