A debt can be assigned (sold) from the original creditor to a third party. A legal assignment under s.136 Law of Property Act 1925 transfers the debt absolutely if: it is in writing, is absolute (not conditional), and written notice is given to the debtor. Without proper notice, the assignment is equitable only.
Legal reference: Law of Property Act 1925 s.136; Consumer Credit Act 1974 (consumer debts); UK GDPR