Naval construction as Depression-era policy

Would building cruisers and destroyers have made sense as a way for Britain to reduce the effects of the Great Depression?

Yes. Britain already used cruiser construction in part to support industry and employment while renewing the fleet.

Fleet renewal could also serve economic policy. Town-class and other cruiser programmes sustained shipyards and employment while providing ships the Royal Navy needed. Britain therefore had useful naval work available during the Great Depression. Political choices about allocating money, rather than a shortage of worthwhile designs, set the limit.