The Bulletins of State Intelligence were supplements to the [London] Gazette where you can find military and naval exploits culled from the main paper and presented without the “clutter” of many of the other news items. Originally named the Bulletins of the Campaign, the title later morphed into the Bulletins and Other State Intelligence. The above highlighted link contains all three titles in an almost complete run from 1793-1883. As far as I can tell, each volume has its own index; I have not found a cumulative index as of yet.
Naval Exploits from the London Gazette