flesh out its territorial claims

What is the exact meaning of the following passage? It is from the book “Persian Gulf Command” by Ashley Jackson, p. 3:

For the British, the region had to be defended because of its oil, and through the fog of war London descried a new moment in the Middle East, an historic opportunity to flesh out its territorial claims across the great arc from Suez to the headwaters of the Persian Gulf. What transpired was an impressive last hurrah of British imperialism before its precipitate post-war decline.