In 1944 HMSO published a pamphlet called 'The Air Battle of Malta. It has many good photos, though the text has to be taken with a pinch of salt after the propaganda merchants and censors had had their go. On page 12-13 there is a map of the eastern section of the island, and it shows the airfields of Malta: Takali, Luqa, Safi Strip and Hal Far. Hal Far appears to be just a field, but Luqa had four runways, Takali three, and Safi two. Between Luqa, Safi and Hal Far are lots of squiggly black lines showing the dispersal pens and the roads between them; and yes, it appears to have been possible to taxi, in a meandering manner, from Luqa to Hal Far. The vertical photo of Takali posted in this thread is similar to, but not quite the same as, a photo on page 44-45.
If you can get a copy the booklet is worth it for the photos alone. My father was out there twice, in late 1941-42, very briefly, as a Whitley W/Op.