Since "Anglo-Saxon" (Old English) hasn't been widely spoken in roughly 1000 years, give or take, your determination to only use "Anglo-Saxon" vocabulary is going to severely limit the subjects which you can discuss.
Furthermore, you start with a rather peculiar assertion: "It's often said that the best writing chooses Anglo-Saxon vocabulary instead of lofty Latin or french words." You wouldn't care to produce a few examples of that advice, would you? Certainly I've never heard it said, and I suspect that whoever has been filling your head with advice has no idea where most English terms actually come from. Most likely it is actually a criticism of excessive use of Latin and French phrases which some folk use to try to impress, but that by no means suggests that more basic Modern English terms are somehow "Anglo Saxon". Equally important, few of the Old English words which have survived into Modern English did so unchanged.
Anyone who tells you otherwise is feeding you a line of bula.
EDIT - With the example given, you need to be aware that the writer was, I regret to say, being very loose with his terminology, and "Anglo Saxon" was used as shorthand for Old English words which have been incorporated successively into Middle English, Early Modern English and Modern English - and usually changed along the way. A good example is found in the article, where he contrasts "lying" (good old Anglo-Saxon plain speaking), with Churchill's "terminological inexactitude". The only problem is that "lie" in Old English is "licgan". To make the matter worse, the article uses "He eschewed Anglo Saxon and brought down the house", and "eschew" is traced to either the French "eschiver" or the Germanic "schuen". In this case he allowed himself to be trapped into violating his own advice by the shadow of the classic phrase "eschew obfuscation", and would have been truer to his own thesis (although less amusing) if he had used "avoided".
With all this said, in response to your original question there is no need to find a listing of "Anglo-Saxon" vocabulary. Just follow the advice in the article: "It almost always will be short rather than long, plain rather than ornate, simple rather than complex." In other words, pick the simplest word you know which expresses the meaning you want to convey. Look at the examples given. Do you really need a reference to tell you that "do" is simpler than "perform", or "house" is plainer than "habitation"?