What is the best-known book set on Malta?

See note on methodology

It took a little calculating here, but there is a very clear winner once all editions and collected works are taken into account. A sixteenth century play, a story of religious conflict, intrigue, and revenge, focusing on a particular religious minority on the island, it is not its author's best-known work but it is certainly the best-known book in the English language which names the place in its title. It is:

The Jew of Malta, by Christopher Marlowe

Three books set on more recognisably realistic Malta also scored well, the first two both set in the 16th century, one concerning the adventures of a Scottish knight in 1551 (the third of a long series of novels about him), the other about a more German adventurer in 1565 (the first of a trilogy). They are:

The Disorderly Knights, by Dorothy Dunnett
The Religion, by Tim Willocks

The other is set in a more recent global conflict, a story of murder against the backdrop of the siege of 1942:

The Information Officer, by Mark Mills

Disqualified due to being only partly set on Malta, but would have scored well:

V., by Thomas Pynchon
Treason's Harbour (Aubrey-Maturin #9), by Patrick O'Brian

And that concludes the European Union part of this exercise.