Italian ocean-going cruisers would draw British scrutiny

Would Italian light cruisers designed for ocean operations with 6-inch guns trigger a British response?

Yes; Britain would question the mission behind the ships and consider how many cruisers it needed to station against them.

Cruiser design communicates intended reach as well as technical capability. Italian ships optimized for ocean service would prompt Britain to ask where they were expected to operate and to assign enough cruisers to protect trade and imperial routes in response.