Rejected from UCL Law but...

Per UCL: https://www.ucl.ac.uk/prospective-students/undergraduate/how-apply/after-you-apply#circumstances
They don't consider extenuating/mitigating circumstances themselves at all, they expect applicants to a submit them to their school and exam board(s) and will accept whatever decisions those bodies make in view of the circumstances. This is quite a common policy for many UK universities to ensure they aren't "double dipping" on extenuating circumstances where a student has some positive outcome applied by their school and/or exam board, and then the uni also applies a postiive outcome (unnecessarily as the issue was already remedied at the school/exam board level).
Note they also state on that page that decisions are final and applications will not be reconsidered.
If you really wish to be considered by UCL then you probably need to be looking at reapplying in a gap year, or perhaps seeing if there's a chance they will be in clearing with your course; this is unlikely unless your course is a humanities/languages/non-quanitative social science, or some biological or physical science courses. Popular areas like law, economics, engineering, medicine, etc are very unlikely to be in clearing at UCL and have not been in clearing previously.

Per UCL: https://www.ucl.ac.uk/prospective-students/undergraduate/how-apply/after-you-apply#circumstances
They don't consider extenuating/mitigating circumstances themselves at all, they expect applicants to a submit them to their school and exam board(s) and will accept whatever decisions those bodies make in view of the circumstances. This is quite a common policy for many UK universities to ensure they aren't "double dipping" on extenuating circumstances where a student has some positive outcome applied by their school and/or exam board, and then the uni also applies a postiive outcome (unnecessarily as the issue was already remedied at the school/exam board level).
Note they also state on that page that decisions are final and applications will not be reconsidered.
If you really wish to be considered by UCL then you probably need to be looking at reapplying in a gap year, or perhaps seeing if there's a chance they will be in clearing with your course; this is unlikely unless your course is a humanities/languages/non-quanitative social science, or some biological or physical science courses. Popular areas like law, economics, engineering, medicine, etc are very unlikely to be in clearing at UCL and have not been in clearing previously.

Sorry i meant King's...what their policy