Do I need Planning Permission ?
Some form of written permission is advisable, even where a project is considered to be 'Permitted Development'.
If you are building a smaller extension under 'Permitted Development' rights, it is highly recommended to apply for a 'Certificate of Lawfulness' from the Local Authority to confirm this interpretation is legally correct. This written confirmation is particularly important if your plans are ever queried, perhaps by a neighbour, or by a solicitor when you later come to sell the house.
You can look at the guidance on the Planning Portal to see what might be Permitted Development. As a rough guide, in England you have an allowance of 70 cubic metres that can be added to the rear of your property and in Wales extensions via PD typically cannot go more than 4m beyond the rear of the original property . Outside of these limits, full Planning Permission will be required.
Conservation areas may have stricter controls under a local 'Article 4' designation that limits what can be done to features that contribute to the character of an area, like windows and chimneys, meaning that PD rights have been removed in that area.
Once you have Planning Permission (or a Certificate of Lawfulness), it is important that you build in accordance with the approved drawings as any departure may invalidate the consent granted.
Note that you will always need to make a separate application (or serve a Building Notice) to Building Control or an Approved Inspector under the Building Regulations before any actual construction can begin.