Yes, in most cases you can use an outbuilding as a home office without needing planning permission. As long as the use remains incidental to the main dwelling it is still considered part of your domestic residential use.
A single storey rear extension can fall under permitted development, meaning planning permission may not be required providing it meets certain criteria.
In terms of height, the extension must:
Read about planning permission for extensions on Planning Portal
If you're doing electrical installation work in your home or garden in England or Wales, you must follow the building regulations. It's recommended to hire an installer who is registered with a competent person scheme (a registered competent person’) who can self-certify that the work meets the required standards.
The green belt is a specially designated area of countryside protected from most forms of development. It is protected to help stop urban sprawl, preserve the character of existing settlements and encourage development within existing built-up areas.
The government are working on improving access to public land records, allowing you to check certain restrictions on land. You can view their progress here and see whether your land is greenbelt (note: this tool is currently under development).
You should contact your local planning authority to find out if your land is in a green belt area, and any policies or restrictions that may apply as a result.
If you carry out development without the necessary planning permission, and it doesn’t fall within permitted development rights, you may be in breach of the planning rules. In such cases, you will usually need to submit a retrospective planning application to seek approval for the work already completed or started. However, there is no guarantee that permission will be granted.
Learn more about planning breaches on Planning Portal
You can usually put up new fences, gates or garden walls without planning permission, as long as you stay within permitted height limits. If the structure is adjacent to a highway (including footpaths), it must not exceed one metre in height. For all other boundaries, the maximum permitted height is two metres. Anything taller than these limits will require planning permission.
Read more about fences, gates and garden walls.