You may be able to use your Permitted Development Rights to build such a structure. These allow you to extend your dwelling by a certain volume from the ORIGINAL size that it was built. I won't try and outline all the rules here - but do phone your local council's development control department to ask about it. You are unlikely to have such PDRs if you live in a Conservation Area or an AONB.
Otherwise you would have to apply for PP.
Certificates of Lawful Development are something different. If you erect a structure that needed PP but you failed to get it and you got away with no-one noticing for a minimum of 4 years, the Planning Dept cannot after that time demand that you demolish it. One can then apply for a CLD which 'regularise' the position as if you did have PP all along. In these situations a council cannot refuse to issue a CLD.