35W 6V, what wall wart max current needed
You should not chose the wall wart based on the power it uses on the mains side, but the current it can source on the 6V side.

Generally, if all power converters had an efficiency of 100%, you would put as much power in as you get out, meaning that it would need to draw 35W/230V=0.15A on the mains side. However, since there's no way of telling how efficient an arbitrary power supply is going to be, you will need to grossly oversize this.

By the way, 35W is relatively hefty for a "wall wart" form factor power supply. This definitely sounds more like small laptop power supply.

Please also consider the cabling involved: At 5.8A, assuming a cable length of 1m, the typical AWG 26 cable has a resistance of 0.134 Ohms one way, meaning that 5.8A*2*0.134 Ohms = 1.55V is wasted on heating the copper cable, meaning that less than 4.5V are actually available to your device, if that happens to draw a constant current, but more likely, it will see a inner source resistance of 0.268 Ohms, meaning that voltage at the device will fluctuate with the power it draws. Under no circumstances you'd want that.

Hence: Oversize a bit. Get a power supply that offers at least 6.5A. In fact, on uk.farnell.com I couldn't find a single plug-in supply AC/DC supply for 6V that offers at least 6.66A that was in Stock in Europe. 6V with that much current just isn't very common.