A veritable can of worms here Neuron. You'll get many different takes on this, depending on who you ask.
Yes, applying Diversity will certainly allow the use of 6mm cable plus 32A MCB.
This does assume that the cable really is routed so that no de-rating is necessary.
I think I can safely say that most Electricians would upgrade the cable to a 10mm for the 13.6kw and the 17.1kw, considering that the 17.1 has a potential draw of 71A.
The 32A breaker is the key here. With that, the cable is protected. What Electricians try to avoid is the possibility that at Christmas for instance, the whole lot could be on. Manufacturers know that all elements constantly switch on and off during use (thermostatic). Overload is thus less likely, but no one wants to be called out because the 32A breaker keeps operating due to overcurrent.
I would say that, theoretically, you're OK.......... but ............ I would be much happier if BRIGHT SPARK of this Parish sees this and gives his opinion. Hopefully he'll see this.