In most cases, you won't need to seek planning permission to build a garden office, as long as it adheres to building regulations and permitted development guidelines.
These guidelines state that your garden building must not be used for overnight accommodation, and must be a maximum of 2.5m in height (including the roof) to be exempt from building regulations.
However, you may require planning permission if you:
Live in a flat, apartment or maisonette
Live in an area defined as designated land (national parks, conservation areas, etc)
Plan to build over the permitted height
If you live in a listed building
If anyone is planning to live in the new building