Class 6 (Small detached buildings) of Schedule 2 (Exempt buildings and work) of the Building Regulations 2010 only describes the building (taken as the whole building) as being substantially (a considerable amount of it) non-combustible (not flammable). The principal being not to put a high fire load close to the boundary (it does not differentiate between a boundary to a house or a garden). Copy attached.
When designing controlled buildings in terms of unprotected area (windows, doors, combustible construction) in accordance with the guidance in Approved Document B, then the focus is the relationship between a specific elevation and the relevant/notional boundary. In controlled buildings the walls close to the boundary have to be fire resisting from each side as well.
The timber frame walls would need to be clad internally and externally with a non-combustible material to qualify as being substantially non-combustible (calcium silicate board, or plasterboard). Treatments are also available for exposed timber linings/cladding (Envirograf products, or similar).
If you provide confirmation of the construction, then we can then confirm that it is exempt.