Don't have one, but the Ninja BBQ I've just looked up is rated at 2.4kW, that's a 10A load on EHU, so only going to work on a 16A rated EHU!
Don't forget, if you're in a caravan or MH, there are the background demands like battery charger, lights, pumps etc. also drawing off the EHU, so potentially pushing towards EHU capacity even at 16A! No chance of running kettles, microwave, water heater etc. at the same time.
BUT it gets worse, the 13A sockets in caravans, MHs and on tent hook up cables are protected by 10A rated MCBs, you are pushing to the limits of those! MCB's usually have a bit of latitude to cope with a little overload, but a BBQ may be running for some time and the MCBs may just trip from prolonged load at their full rating.
I personally would not rise running a 2.4kW appliance on a 10A EHU supply for the reasons explained by Monty.
Some sites in UK, also in France and the Netherlands, still have 6A supply!
2.4kW would be the maximum power output at the appliance's highest setting.
I can only assume that the OP had the BBQ at a lower setting when the kettle was turned on, and the kettle could be a low wattage one, and the EHU supply might have been greater than 10A.
Certain information are lacking to be able to explain why the EHU did not trip when the OP had the BBQ and kettle running at the same time.
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