North Herts Council states the conservation area rule in its own words: "The Council requires at least six weeks prior notice of intended works to trees situated in a conservation area. During this period the Council can either give consent for the works to proceed or, if there are objections, make the tree(s) the subject of a Tree Preservation Order. In the event of the Council not doing either of the above within the six week period then the works may proceed." It sets out the exceptions on the same page: "You do not need to notify us if you want to cut down or work on a tree in a Conservation Area that is less than 7.5cm in diameter (measured 1.5m above ground) or 10cm if you are thinning to help the growth of other trees."
For trees under an order the council states that consent is required for all works of pruning and felling, with an exception where the work is urgent and the tree is dead or in a dangerous condition, and that "it is a requirement to give at least five working days written prior notice to the Council of proposed work on dead trees". It also notes that many planning permissions carry conditions protecting existing trees, and that written consent is required for works to those trees. Hitchin has its own conservation area.
Nationally, gov.uk describes the requirement for "people to notify the local planning authority, using a section 211 notice, 6 weeks before carrying out certain work on such trees, unless an exception applies", and says the work may go ahead sooner where the authority gives consent. The same guidance states that consent "is needed for carrying out work on diseased and/or dying trees unless some other exemption applies".
We would explain how you check the conservation area boundary, any tree preservation order and the proposed work before confirming whether a section 211 notice or consent is needed.