I have an appliance that I know draws more or less 16A under 240VAC, but I only have 13A sockets around.
Is there any off the shelf solution?
Diodes are used when linking DC supplies, not AC!
It sounds to me like you need something like this: Ceenorm Link
In the UK, you may have a ring-main, which actually gives you double the current rating on the sockets already, but you may need to change the MCB´s for the circuit. In any case, if you have any doubts, call an electrician! Mains can kill.
Short answer. Don't do it. We're talking about mains power here! Hire an electrician to do it.
Longer answer. I would hire an electrician to change the fuses of that power outlet so that it tolerates 16A. By hiring an electrician you will save your life (and possible other due to the risks with malfunctioning mains power). An electrician will also tell you if you need other wiring and perhaps other electrical outlets.