Would there be any problem

A bit more info George...How long is the diagonal run? Where is it? Why is it on a diagonal? Will it be boxed in?

I can't see any reason why not, it would just *look* weird, but if it's out of the way, there's no reason why you can't have it like that

Is the diagonal actually going to be a smaller bore as the diagram suggests?

no, if youre talking about supply. If drain, it would work but be more prone to blockage than would be best.

NT

Short

Under the stairs leading to the kitchen

Because thats the way I want it,rather than running along the whole lenght of the kitchen on top of the skirting

Probably?

I was thinking it might reduce the flow rate somewhat?

I doubt it, that's MS paint for ya. :-p

as long as a piece of string, or longer?

I had an idea it might be.

how?...there's no rules saying pipes have to be run diagonally or vertically, they just look neater that way, although if you ever go in a newbuild that is having plastic plumbing installed, you'll find that they go in all directions, IE wherever they fit, and into whatever shape the plumber wants to arrange them