When I built my Log cabin which is less than 2.5m in height to the ridge, I was advised by the planning office to seek planning permission because it was within 2m of the boundary fence. This was despite it replacing a shed of the same size in the same place!
From your photos I would suggest that if he is building up to the fence he will need PP. If you have not received the letter that does not mean to say he has not applied and been accepted. Basically if you receive permission approval you have 3 years (I think) to build it or you have to re-apply.
If you go to your local council website, you can search planning applications and their condition by postcode. Slap in your postcode and see if they have applied and the status. If there's nothing there contact your planning office and mention that they might be building a permitted development within 2m of the boundary and they will be on them like a hawk...