Building a Shed/Mini Gym Room - (Block Bricks)

[mobad]

I have hired some builders to knock my old crappy shed down, to build a new bigger brick block type shed, with plaster boards, electrics, roofing, leveling and plastering which in total will cost me £3K.

So far we are at stage one where we have knocked the old shed down but had to leave one of the walls as it was too close to the neighbours fence and if we were to knock the wall down, the whole fence would be ruined.
However the builder has said to leave it, as its in good condition and they will build ontop of it for height and on the side for width.

My question is by keeping that one wall and having the rest of the walls as completely new, should that be a problem?

Heres the pic of how it is now -

 

[Woodster66]

Why not remove the fence temporarily, knock it down and replace the fence when the job has been completed? The fence looks as though it is falling down anyway!

Personally I wouldn't be happy with leaving the one wall especially when they have knocked down the other walls already, if the wall is going to be longer and higher then the footings will have to be suitable to take this extra weight, or else you could find it cracking through the blocks. so I would knock it all down and start from scratch.