Do I require permission for a Conservatory?

A conservatory attached to the house will be treated as an extension and
Rules A - F in Section 1 “Building an Extension” will apply.

A free standing conservatory will be considered under the Rules in Section 6.

Do I require permission for another dwelling attached to my house, e.g., a granny flat?

Yes, if it is a separate and self-contained unit. If it is not self-contained it will be treated as an extension and Rules A - F in Section 1 “Building an Extension” will apply.
 

Do I require permission to convert my house, or part of it into one or more flats?

Yes, even though building work may not be involved, this will be treated as a
change of use.
 

Note 6 - The use of any part of a house as an office or for commercial purposes
may need planning permission depending on the nature and scale of the use. Check with your local planning office.

Do I require permission for to demolish part of my house or a shed for example?

Only if your house lies within a Conservation Area where consent would be required for the demolition.