I agree that a new radial should be installed as this appliance would be on for long sustained periods. But what constitutes a "fixed load"?
Appendix 15 suggests loads such as cookers ovens and hobs. I would imagine as these can be a substantial load on a ring final over long periods.
Appendix 15 gives suggestions as to how the loads on ring finals can be reduced, and that is by taking larger loads off the ring.
At no point does is say "must" but given the nature of this load a good designer would put in a separate circuit.