FIRSTLY. In most cases the answer is no but it will depend on size, height and use.
You can build many structures, including a Garden Room under ‘Permitted Development Rights’ . This means that would not have to apply for planning permission. However there are some limitations: If you are closer than 2M to your boundary your building must be under 2.5M from the highest point of the adjoining land, and must not cover more than half of the garden space. This is the most common scenario. However, if you can build more than 2M from the boundary then you are allowed to build up to 4M apex height for a dual pitched roof, or up to 3M for a single pitched roof, but in both cases the eaves height must not exceed 2.5M. Any building should not be used for overnight accommodation. This is a VERY simplified version of the rules and please check out the full descriptions at: https://www.planningportal.co.uk/permission/common-projects/outbuildings/planning-permission
If your ideas fall outside of these conditions (eg you want to build higher than 2.5M) then you can still apply for planning permission in the normal way.
SECONDLY. Notwithstanding Planning Permission, you will still need to consider Building Regulations. The main concerns here are as follows:
A Garden Room up to 15M2 does not need to comply with Building Regulations, and can be built close to the boundary on all sides.
A Garden Room 15 – 30M2 (internal size) should be built at least 1 meter awayfrom the boundary on all sides OR must have non-combustible materials on the adjoining walls. In practice, it is reasonably easy, but a little more expensive to comply with this.
A Garden Room over 30M2 (internal size) will come under building control, and must be notified and checked by the local authority.
More information can be found on the Planning Portal website above: look at the left-hand menu about Building control.
It is the responsibility of the householder to ensure that Planning Regulations and Building Regulations are followed.