Consider access to said chalk stream, OP.
The big estates, landowners and fishing clubs like to keep their extensive river sections very private on the classic fishing chalk rivers, which means in many places you are restricted to glimpsing the river at a distance and occasional crossing points. Those managing those areas are absolutely not chilled about sharing their passion and love of the natural environment with casual trespassers – it’s basically their fishy golf course. Test Valley is really not great in this regard, worth bearing in mind.
I’d consider the Itchen upstream of Winchester, middle Hampshire Avon and even wildcards like the upper Kennet and Lambourn being better options than some of the ‘classic’ chalk stream tourist hotshots, unless you are connected 😉