Any fixed appliance over 2 kw would if following the appendix in regulations would need dedicated circuit.
It is normally considered that 3 kw is the limit for a 13A fuse. However they will allow a far overload before blowing and as an emergency while waiting for electrician to install correctly likely it would work.
Also likely the fuse would blow from time to time.
I would not plug one in myself. Mainly as even with 13A plugs over time do seem to fail. However I have seen the old 15A sockets used for immersion heaters and like so that maintenance people can unplug and replace without the need for an electrician. However it would still need to be on a dedicated supply.