From 1810 to 1813, the Ionian Islands were under British protection as part of the United States of the Ionian Islands. During this period, the key governors were:

1. Sir Alexander Ball (1808-1810) - Before 1810, Sir Alexander Ball was an influential figure. Although he officially left before 1810, his governance and policies greatly influenced the early 1810s.

2. Thomas Maitland (1812-1823) - Although Maitland began his governorship in 1812, his role was significant throughout his tenure. He was appointed as the Lord High Commissioner of the Ionian Islands. Maitland's governance was marked by his firm control and implementation of British administrative practices.

There were likely interim administrators during transitions, but records point towards these figures as key governors impacting the period surrounding 1810-1813.

For further detailed reading on this topic, consider exploring historical texts related to British colonial administration or the history of the Ionian Islands.