Lean-to shed advice

[NGEddie]

I have a space in my garden that would be great for a shed, but I'm not sure the best way to fit it in. I've included a picture below, you can see it's behind my garage and has a fence on one side and the brick side of a conservatory on the other.
The triangle conservatory windows you can see are only 2100mm high, which wouldn't be very much headroom and wouldn't allow the garage door to open, so I'm considering having a apex peak as shown in the picture.

Problem I'm looking for help with is how to handle rain water in that scenario?


Or any other suggestions if this isn't the best way to go?

 

[big-all]

as your neigbour already looks like there water sheds onto your side off the fence my thought would be a flat roof clearing the door thus going part way up the glass side panel terminating the opposite side at the same height as there roof and sharing a gutter
you also need to keep it below 2.5m to avoid planning permission
without having a seperate floor installed you will get a permenant damp problem

 

[NGEddie]

as you say, for the roof to slope from right to left it would need to start above the current brick line, by the window. How to make that work and be water tight? Would you build a wood wall on that right side? Rain drainage then become a problem.

 

[big-all]

my thoughts
have a beam going from a point right beside the lh side off the door 12mm higher than the door towards the outer wall nearest where you stand taking the picture with a near flat roof section between the beam and under the window lip with batons supporting the roof from the rh side off the door and under the windows
hopefully it will have enough drop to stop water pooling
with possibly additional timbers between beam and under the window clear off the arc off the door
this will off course give you a duel pitched roof