The FCA's Dispute Resolution: Complaints Sourcebook (DISP) outlines how complaints should be dealt with by firms, payment service providers, electronic money issuers, CBTL firms, designated credit reference agencies, designated finance platforms, VJ participants, and the Financial Ombudsman Service.
Recordkeeping requirements for the above entities can be found throughout DISP. DISP specifically requires record retention of MiFID complaints and complaints regarding: handling rules, complaint resolution rules, complaints that are resolved by the close of the third business day, complaint time limit rules, complaint forwarding rules, and complaint time barring rules.
Link to FCA's table of recordkeeping requirements found in DISP: https://www.handbook.fca.org.uk/handbook/DISP/Sch/1.pdf
Link to DISP Handbook: https://www.handbook.fca.org.uk/handbook/DISP.pdf