I currently have an awful kitchen extension with a monopitched roof,
that was built by the cowboys from hell and has no redeeming features at
all. It has to go. If I have to replace it, I'd like it to be bigger,
as it is currently a 6m wide by 2.8m deep (i.e. towards garden) galley
kitchen which doesn't really suit a quite big semi.

The neighbouring semi has a flat roofed extension, but I would very much
like to avoid this from a practical perspective as well as aesthetic.
The difficulty is that to extend the depth of the kitchen further into
what is now the garden means that the current monopitch roof can't be
replicated, as there is insufficient height under the first floor
window. There would be enough height for a pitched roof with the gable
end pointing out towards the garden and the slopes heading down toward
the side of the house (on the detached side) and the next-door flat roof
extension on the other side.

My question is, is the a usual way of dealing with this situation? The
slope that abuts the neighbour's wall will need a draining htvalley at
rig angles to the main slope, so that the water flows down toward the
garden. Can anyone help with how is this done, because I am finding it
hard to envisage?