The OP said his friend told him 16 would be needed and I don't think anyone has queried it. t should be discussed with the electrician.
Agreed - that's why I wrote "True" and also wrote that the OP required input from an electrician
If there are things that need bonding in the outhouse (there's obviously going to be a water supply, but it might enter in plastic), there are clearly decisions to be made about the earthing arrangements,
It would be easier to install a section of plastic pipe.
IF a metal water pipe were the only extraneous-c-p, then I agree.
and if the house's equipotential zone were all beingt 'exported',
Extended

If the pipe comes from the house ???
Unless it's very old, I seriously doubt that the bulk of the (assumed underground) run of water pipe would be metal - although the bits emerging from the ground at the ends might be. That's how the water supply to my greenhouse works - nearly all plastic, but two or three feet of copper (partially underground) at each end.
then the CPCs of either 10mm² or 16mm² would clearly be inadequate (I'm not sure, without looking it up, about SWA).
Have I missed something? Why would such CPCs be required?
IF (on electrician's advice) the house's 'earth' were 'exported' to the outhouse, and if there were extraneous-c-ps in the outhouse, then there would be a need for a
bonding conductor back to the house's MET. I was saying that no T+E has an adequate CPC to serve such a purpose.
Kind Regards, John