South Gloucestershire Council says a tree preservation order makes it unlawful to prune, damage or destroy a tree without the council's consent, and that a conservation area tree with a stem of over 75mm in diameter measured 1.5 metres above ground level needs "6 weeks' notice before pruning or completing any other work". The same page says applications go on the planning portal or on a downloadable tree works application form.
The Planning Portal says an outbuilding may qualify as permitted development on an eligible house, subject to all applicable conditions. Among the selected conditions it sets: no outbuilding on land forward of a wall forming the principal elevation, single storey with a maximum eaves height of 2.5 metres and a maximum overall height of four metres with a dual pitched roof or three metres for any other roof, a maximum height of 2.5 metres within two metres of a boundary of the curtilage, no verandas or balconies, platforms no more than 0.3 metres in height, and no more than half the area of land around the original house covered by additions or other buildings. It also says outbuildings within the curtilage of a listed building require planning permission. The same page says that on designated land buildings, enclosures, containers and pools at the side of a property require planning permission and that the allowances do not apply to flats and maisonettes.
South Gloucestershire Council puts the number of conservation areas in the district at 30, names Hanham Abbots, Warmley and Siston among them, and says it may restrict permitted development for particular classes through Article 4 Directions.
We would explain how you check the conservation boundary, any tree preservation order, any Article 4 direction and the proposed work before confirming whether permission or notice is needed.