Fortunately where I live an observatory is considered permitted development by the Local Authority providing it’s single storey with maximum eaves height of 2.5 metres and maximum overall height of four metres with a dual pitched roof or three metres for any other roof.
I had planned to elevate my observatory in the centre of the garden which would have made it taller than 3 metres so modified my desires. Unfortunately my wife’s conditions required that the building not be on view from any window at the back of the bungalow, which was a far more serious constraint. Our garden does extend around one side of the properly so that was the only “permitted” location. This placed it in amongst the greenhouse and other sheds which was not ideal because they caused restrictions on the amount of sky viewable, but there it was erected. However, that was 25 years ago, now most of my neighbours either have bright garden floodlights or illuminate their gardens at night so having the observatory tucked away in the shadow of other buildings has proved very useful indeed.
I have since thanked my wife for being so farsighted!