Oops! forgot to ask what the Supply characteristics to the consumer unit were, so I can sort out the disconnection times properly. Would need the earthing type, TT, TNC-S, TN-S or what not. If it's TNC-S we won't need you to measure the Ze as the Distributor should keep it below 0.35 ohms.
Assuming TNC-S; I'll give you a 'rule of thumb' option;
PVC T&E cable in trunking at 75% de-rating to cover most eventualities we can't see on here. This is probably well OTT. At least with 4metres voltage-drop will not really be a factor.
Demand 7.8kW (never mind what bits are on it it's the manufacturers max load rating for the whole unit you should use). So you need to supply 34amps to the load. Its in trunking on a wall so method 3 would be used. 6mm T&E will only do 38 amps max which if de-rated on a rule of thumb would be 28.5 amps. So the rule of thumb would give next size up at 10mm/52amps derated to 39amps. You may find it a bit difficult to get a breaker to suit this.
Now you need to see if working it out for the actual load would be better. If we can find out that a 40amp breaker would protect the cable ok, then the shopping gets easier.
I'm going to assume it's not runnning anywhere hot, such as wire behind heating pipes or sharing a cavity with them or a boiler flue etc. So correction factor Ca will probably be discounted at 30deg, it could even be a plus at 1.03 but I'm not assuming that here without measuring it. Ci doesn't apply either as you don't mention any insulation. Cg grouping factor won't play as you've only got the one T&E cable. You mention a "Fuse Box" but you may just be using the term to cover a consumer unit. I'll give you options for both.
The
semi-enclosed fuse (BS3036) factor would kill our rating game and send us back to dividing by 0.725. So our only other option would be to leave out the trunking and clip the cable direct. This would give us Method 1 for calculating the capacity of the cable. Now we can take it as 63amps x by our worst cable correction factor of 0.725 or 45.6amps, well protected by a 40amp fuse wire (if you can find one) 45amp (1.25mm) is more common, but would still protect our cable. Now you know that a
10mm cable if clipped direct and not enclosed in trunking for more than 33cm will be capable of supplying the required current to your load. (can't remember wher that length comes from, so maybe one of the others can remind me).
If you mean a consumer unit then you'll be back in the calculation game again.
It'll be a simple method 3 with voltage drop and power factor corrections as per pages 208/209 of your regs book. (I ain't bothering here it's coffee time)
A rough calc from Table 4D2A against voltage drop may get us away with using a 6mm cable if you can find a 34amp MCB and leave out the trunking again. But for the sake of pennies difference and margin for error I wouldn't even go there.
10mm cable in trunking, not running anywhere over 30degrees, on a 40amp MCB will supply up to 52amps so you know you're there with that.Why have I bothered..... well you'll be doing this soon so it's worth having a look at before you go full on into it. Also in the DIY forum it's no harm to show people that there's alot more to installing electrical circuits than just smacking in a bit of wire that looks big enough and hoping for the best. Not that they shouldn't do it, I reckon they should but do it right and do it well if you're gong to DIY.
PS that's just the current carrying capacity. Next you've got to see if the load will disconnect in time if there's a fault.............. 'back on your heads sinners! tea break's over'