South Gloucestershire Council says "Tree preservation orders make it unlawful to prune, damage or destroy a tree without our consent." On conservation areas the same page says "If a tree has a stem of over 75mm in diameter when measured 1.5 metres above ground level, you must give us 6 weeks' notice before pruning or completing any other work", it lists circumstances that do not need permission including a dying, dead or dangerous tree with five days' notice and a fruit tree cultivated for fruit production, and it adds "Even if permission is not required you must inform us that you are undertaking the work."
The same council says that in a conservation area planning permission is needed to "demolish a gate, fence, wall or railing over 1 metre high next to a road, footpath or public open space or 2 metres high elsewhere", and to "erect a building within the grounds of the dwellinghouse that would be situated on land between the side elevation and the boundary". It also says it may restrict permitted development for particular classes through Article 4 Directions.
The Planning Portal says decking may qualify as permitted development for eligible houses, subject to all applicable conditions. Among them, none of the decking or platform is on land forward of a wall forming the principal elevation, it is no more than 30cm above the ground, and with other extensions and outbuildings it covers no more than 50 per cent of the garden area. The same page says no decking or platform is permitted either side of the house on Article 2(3) designated land, that none is permitted within the curtilage of a listed building, and that the allowances apply to houses rather than to flats and maisonettes.
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.