So after some frank and open discussions with our neighbours we realised our original proposal to extend beyond the existing rear wall of the house was pretty unfair (and honestly quite ugly) from their perspectives. It would have cut out a lot of light to one of our neighbours’ patio and been unsightly for the other.
So, we’ve decided not to extend beyond that current line – and will now just be putting a side-return into the “alley-way” with a sloping roof and squaring off the existing patio doors.
We’d like for the new glass patio doors to run across the entire width of the back of the house – but we’ll see if budgets and practicality allows!
The following drawings attempt to show what it would look like in the context of the neighbour’s houses (to the left and right):

And a higher-level view for clarity: