Outhouse Electrical Supply

[snapshot25]

Hi, a while ago we did some landscaping in the garden and laid a single length of 6mm 3 core SWA cable underground in pea gravel from the house CU to an outhouse in the center of the garden (20 metres). Then 4mm 3 core swa another 20 metres from there to the end of the garden (40m total from house). We never got round to having an electrician come to terminate or connect anything. We're currently deliberating over building a summerhouse at the end of the garden with a shower room, in there, I'm thinking about an 8.5kw one of these: http://www.ukhps.co.uk/products/Zip-Instantaneous-ILX009-
for the shower and sink and I'm trying to decide whether the 4mm cable can supply the load for this. At the house CU would be an 60a RCD with 50amp MCB to the outhouse where the 6mm terminates in a CU with a 15amp MCB for a couple sockets and 6amp for light. OK there, now, what I'm not sure about, is, can I put one core of the 4mm swa to summerhouse on 40amp MCB for the water heater and a 20a MCB to supply the other 4mm phase for a few sockets (lights on 5amp FCU).
I've checked what the TLC cable calculator says, and it recommends 4mm for an 8.5kw load over 20metres with 3.2% voltage drop at 37amps, but not sure if it is possible to have 2 phases on 3 core swa with a shared neutral? Does the combined load need to be less than 40amps, or can the shared neutral handle, say 50amps? Is there a lower current option for heating water-would a small tanked heater work for this setup, in which case it would only be 5kw
The summerhouse would be used only when guests stay, so it's not like it would be in frequent use, but would have a 13amp heated towel rail with frost protection thermostat

If it helps, the house has 25mm meter tails, 100a lead-paper supply and an 18 way split-load board with 2x60a RCD's, so I'd have a separate RCD unit fitted for the garden with separate tails from henley block.
apologies, that's a bit waffly.
thanks, and just to clarify, I would be getting an electrician to be doing this, just want to know what's possible first.

 

[ban-all-sheds]

1) What's all this talk of 2 phases? You only have 1 with your supply.

2) You can't put 6mm² cable on a 50A breaker.

3) You don't have an 8.5kW load in the summerhouse, you have 8.5kW + lights and possibly other items, so 4mm² is too small.

4) You appear to be ignoring the voltage drop along the 6mm² cable from the house.

5) How deep are the cables buried? Is there warning tape above them?

6) Do you have a TN-C-S supply, and extraneous-conductive-parts in the outbuilding(s)? http://electrical.theiet.org/wiring-matters/16/elect-inst-outdoors.cfm?type=pdf

7) Building Regulations approval, water/sewerage undertaker permissions, possibly planning consent....

I would be getting an electrician to be doing this, just want to know if it's possible first

At first glance no, but see what people who come to look at the job say.

 

[Taylortwocities]

Why would you want a shower in a summerhouse 40 metres from the main house?
Do you plan on getting so dirty doing the gardening that SWMBO won't let you back into the house until you are clean?

EDIT: just read all of your post
If this is to be living accomodation then you have other loads too:
eg space heating, other lighting, loads on sockets etc.
You need to add up all of the loads and you'll soon see that the cables you have had laid are not going to be big enough.

In general per BAS above plus:

You cannot share the neutral, so that is not an option.

A small Megaflo (eg) with an immersion (3KW) is your only practical option but you'll be paying for the tank to be heated all the time.