If you are somewhat familiar with the German academic system, you might be aware that different disciplines award different types of doctorates. While the list at the German language Wikipedia is quite long, you normally encounter only a few (as listed in the English language Wikipedia).
Three very common doctorates are the Dr. rer. nat. ("rerum naturalium") in sciences, the Dr. phil. ("philosophiae") in humanities, and the Dr.-Ing. in engineering. For Computer Science, which type of doctorate you are awarded depends on your university: Most departments award exclusively a Dr. rer. nat., some exclusively a Dr.-Ing., some allow the candidate (or the advisor) to choose between the two, and a few do something totally different (again, see Wikipedia).
When my alma mater, Goethe University in Frankfurt am Main, was founded back in 1914, the physicists did not want the Dr. rer. nat. for their department. Translated literally, "rerum naturalium" means "natural things", and one of the founders claimed that you can only be a doctor of a science, not a thing (where I use "science" as translation of the German "Wissenschaft", which does not distinguish between humanities and natural sciences).
Thus, Goethe University decided to be the only university that uses Dr. phil. nat. instead of Dr. rer. nat. as abbreviation of "Doktor der Naturwissenschaften". (This story was apparently forgotten and re-discovered by the university archivist in the early 2010s, at least according to the university newsletter.) Decades later, Computer Science was introduced, and as Goethe University has no engineers, the natural sciences doctorate was the natural choice.
To cut a long story short: "Dr. phil. nat." means "Actually a Dr. rer. nat., but from Goethe University, because we are really unique and special".
But all that is outdated anyway. In December 2014, Computer Science and some other departments switched to rer. nat., which means that, after a transition phase, there will be no more Dr. phil. nat. in Computer Science.
It's not important anyway, especially not when living in Britain. Here, people are so efficient that they don't care about rer, phil, or whatever. In fact, they don't even write "Dr.", and use the much shorter "Dr" instead. Neat. (And you can use it in dropdown lists as a gender neutral title, allowing you not to choose between Mr/Mrs/Ms/Miss, if that's your thing).