No, not going to be left alone with children.
Cleaners come, cleaners go, some may last a while others may not. So unless they become a permanent feature, I can't see the regulator requiring them to have a DBS check, as long as they are never alone with children.
Could cleaner come at a time when children are not present? That way they are never in contact with minded children.
Some cleaners will have a CRB/DBS check as cleaning agencies may have done that, so if that is the case make a note of the disclosure number if they let you.
Certainly check ID and make a record of basics like name, address.
Ask regulator for advise if cleaner stays several months, as then they become a frequent visitor. DBS check will cost you, probably around £60.