Yes, the 4mm^2 refers to the individual conductors. The current carrying capacity of a cable is affected by the type of cable (i.e. SWA is different to T&E, and there are even multiple types of SWA depending on what insulation is used), and what route (properly termed installation method) is used (e.g. burying it underground will be different to clipping it to a wall).
Once you have the current carrying capacity (the TLC calculator will give you this), the maximum VA it can carry is obtained by simply multiplying the 'A' figure you've got, by the voltage (nominally 230V, in reality is normally 240V).
As well as the current carrying capacity, there is a limit based on voltage drop - the longer the cable, the more volts it will drop, so you sometimes have to put a bigger cable in to avoid the voltage drop being too high. The TLC calculator takes this in to account when you specify the length of cable...