Root cellar - permitted development?

[TCO]

I'm looking to add a root cellar to an existing property.  The entry to the cellar will be separated from the main building by a path and the cellar will extend away from the building - ie it isn't connected to the main building in any way.  The cellar will extend less than 8m total from the existing rear elevation and the property is not on article 2(3) land.  The cellar will all be directly to the rear of the existing building (ie doesn't extend to either side).  Does this fall within class A permitted development?

 

The cellar has dual purposes.  One is as a root cellar, for storing apples and vegetables grown during the summer.  It is also intended to house a small water tank, pumping, filtering and sanitising equipment for the household water supply, all of which is currently above-ground.  Does this fall within class E permitted development?

 

My local council is B&NES.

 

Many thanks for any advice.