Assuming that it was a private flight, Part-CAT is not relevant. You need to refer to Part-NCO:
NCO.IDE.A.140 Seats, seat safety belts, restraint systems and child restraint devices
(a) Aeroplanes shall be equipped with:
(1) a seat or berth for each person on board who is aged 24 months or more;
(2) a seat belt on each passenger seat and restraining belts for each berth;
(3) a child restraint device (CRD) for each person on board younger than 24 months; and
(4) a seat belt with upper torso restraint system on each flight crew seat, having a single point release.
This assumes that the state in which it all occurred had implemented Part-NCO (the UK hasn't). If Part-NCO had been implemented then the aircraft was not fit to fly without a serviceable torso restraint system in the flight crew seat. If Part-NCO had not been implemented, you would need to examine national legislation (if any).