Kirklees Council lists 60 conservation areas. The Huddersfield ones include Almondbury at number 12, Edgerton at 13, Quarmby Fields at 14, Greenhead Park at 32, Huddersfield Town Centre at 36, Longwood Edge at 38 and Scholes at 42.
For extension work the governing document is the council's House Extensions and Alterations Supplementary Planning Document of June 2021, which implements Local Plan policy LP24 on design. It runs on a comply or justify basis: the council says proposals that comply "are more likely to progress through the planning process quickly and successfully", and that those departing from it "will need to provide a full justification".
Its single storey rear extension guidance is that an extension should not project more than 3 metres from the rear wall of the original house for semi detached and terraced houses, or 4 metres for detached, should not exceed 4 metres in height, should keep eaves below 2.5 metres where it exceeds 3 metres in length, and should retain a gap of at least 1 metre from the boundary. Two storey side extensions should be set back at least 500mm from the front of the original house and keep a 1 metre gap to boundary walls. Where the house is listed or in a conservation area the council recommends a formal pre application enquiry.
We would build a page that quotes the SPD figures, explains which jobs need permission, and says that you check the address against the conservation boundary before you quote.