If you're looking to complete your degree you're probably going to need to look to do so elsewhere.
If it was an undergrad course depending on the exit qualification you may be best off looking at bachelors top-up courses or credit transfer at the OU if you got a DipHE. If you got a CertHE then you may just want to look at applying to first year at another university (but probably should strongly consider another, unrelated subject, unless the reasons you were required to take the exit award were as above, completely out of your control). This seems to be more or less the gist of the KCL format but again, might be a hard sell to return.
For postgraduate courses not really sure honestly. If you have a PGCert/PGDip then you could just apply again to another masters degree elsewhere (or somehow at KCL still) I guess but, the costs may be prohibitive. If you had an exit award from a PhD then that might really be the end of that process from what I've heard.
Note also the KCL regulations make it very clear they reserve the right to not allow automatic progression at all and could well say you need to start from the beginning again (if they make you an offer again at all).