Stevenage has seven conservation areas: Broadwater, Old Town High Street, Orchard Road, Shephall Green, Symonds Green, Town Square, and St Nicholas and Rectory Lane. Each has its own Conservation Area Management Plan supplementary planning document. The council's tree page asks you to contact it "to ensure that the trees are not protected by a Tree Preservation Order, planning constraints or that the tree is within a Conservation area", and points to the Planning Portal for consent under an order.
The council does not state the notice period on its own pages. 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".
On felling, the Forestry Commission states that a licence is needed to fell more than 5 cubic metres in a calendar quarter where the trees are over the diameters it names, 8cm over bark measured at 1.3m above ground, or 15cm for coppice or underwood, and that "You can sell up to 2 of the 5 cubic metres per calendar quarter. If you sell more then you will require a licence." It lists further exceptions, including work to prevent danger or nuisance. Licences are free in England.
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.