What causes a water swishing noise in the bay of a subaru Impreza which recently had new radiator fitted?

Water swishing noise may be due to a seriously underfilled radiator-- the shop rushed the job and did not clear the air pocket inside the engine. With cool engine, remove radiator cap, and ensure the coolant is right up to the lower lip of the filler neck. Replace cap, and drive. Recheck again the next time engine is cool. Also, make sure your coolant reserve bottle is at least 1/3 full when cold. Remember, never remove a radiator cap when the engine is at all warm.