The timber shed will have a limited life unless it is made in hardwood and it will then be so costly that a concrete block building may be preferable.
The buried PVC box is very inflexible and not really suitable for automatic chlorination because of the access difficulty with dangerous chemicals.
Economical prefabricated timber buildings for the pool plant room are often available from local suppliers – look out for special offers.
A concrete block building with a single slope roof should cost in the order of £2000+ and provide enough room for the pool plant (as well as your deck chairs etc).
The plant room can be used to store all your poolside furniture in winter and/or changing & shower room facilities. If the pool is near an existing garage or barn the pool plant can go in there (about 2m² of floor space is required for the pool plant and filtration system).
The plant can be buried underground in the PVC box (as pictured) with green PVC hinged lids for access.
Pool installers do not like them much because of the slightly difficult access to the pool filtration components but they do work well. Just make absolutely sure that the pool installer does not drill holes in the box that might let in water. Believe me this can and does happen!
They have the other drawback that if any of the plumbing connections leak, the plant housing can fill with water and cause the electrics to short out.
Electrical switchgear must not be located inside buried plant housings.
If the land where the pool is to be built has quite a cross slope then a below ground plant room, built in concrete blocks, is sometimes possible. Costs will vary but are unlikely to be less than £3000.