Henryp wrote:

There seems little in verse or song to commemorate Anson, a naval hero.

Firth's book of naval songs offers "The Lucky Sailor, or The Sailor's Invitation to Go with Admiral Anson." This is also in Palmer's "Sea Songs." It's Roud #V22822. There is a broadside in the Madden Collection.

There are also some songs which are sort of Anson-adjacent, such as "Bold Hawke." The best-known of these is surely "Warlike Seamen (The Irish Captain)," Roud #690. The "Captain Somerville" (or whoever) of that song is actually Philip Saumaurez, who was one of Anson's officers on his world tour. It was Anson's support that earned him his captain's rank and the command of the ship in the song.