Hi, I fully understand your concern and wanting to help her out, but to be honest she could have a go at trying to sort this out herself, she'd probably have a lot more info to go on than you do (look through her emails, on the Kings portal, etc).
This page, easily found on Google, tells you what to do: www.kcl.ac.uk/study/dbs-clearance-check. If she's not yet enrolled, contact the Admissions Office. If she's already enrolled, scroll down to "Faculty Contacts" and click on the relevant contact info.
If you have a quick Google, you can also find other emails for the various departments within her faculty (eg law would have law general, law admin, law assessments, etc email), and you can cc all of them as well if you're desperate.
If she needs further signposting, she can contact student services. If she already has the login, put in a request on the KCL student services portal. Otherwise/in addition, it would be faster to contact them on the helpline (they'll be open till 4pm today) or webchat, or even better, drop-in (walk-in will be quicker than booking an appointment, though she'll have to wait) on campus.
According to an email they sent out, Kings' student services just re-opened on 9 Jan and they'd be overwhelmed with service requests from students (especially international students) over the xmas break. I'm guessing it's much the same for all the other staff.
It's good to speak to her personal tutor about potential issues with her course, but do note that academics aren't actually responsible for admin etc.
Kings admin are very helpful (especially compared to other uni admin like at UCL) but extremely inefficient... However if there are major screw ups (which both I and my course mates have often faced), they will make provisions for your daughter to catch up without any impact on her course progression or grades.