Anglo-Saxon is better known as Old English. Generally, modern English speakers are not able to understand it without training. You'll find a couple of examples in this thread: excerpts from the famous epic poem Beowulf, and the Bible

• I can partially understand Middle English readings of Chaucer, while Old English sounds entirely foreign to me. How easily would a speaker of Middle English (14th century) be able to understand an Old English reading of Beowulf (9th century)?

Edit: a few more examples here

• If I was to go back in time to Medieval England (c1000) and visit a rural hamlet, would I be able to have conversations with the locals? What about London?

Largely, no. You might be able to find some similarities in a few nouns but sentences would be entirely incomprehensible. Even words which look similar in written form would probably be pronounced so differently that you would not recognise them when spoken.