I'm an architect (I work for the practice that designed the main Horniman extension building), and I agree with Michael and thenutfield. Old buildings shouldn't be saved just because they're old, but because they are of merit - architecturally, functionally and socially.
We're used to working with old buildings, some of them exceptional and some pretty grotty. The crucial question here as far as I can see is not whether the old pool building should be saved, but what is the design for the new pool.