Bang on Jackie. Over to you.
It is indeed the Lillies, and the smaller blacked out name is Lily Creek. One little fact I meant to mention: it is here that the direction of buoyage changes. As you travel west along The Swale, red cans are on your left (port) and green cones on your right (starboard), however once past The Lillies red cans are to your right, and green cones to your left. Confuses trainee sailors like mad!
The map is the OS 6" County Series published between 1830s-1880s. This particular sheet is Kent XXI, Surveyed: 1865, Published: 1869. Pulling out slightly and with no blanking: