AD 800 is a tough period to study in western Europe for clothing, because very few garments survive (and those that do are just fragments). So everything we know about clothing from the period has been pieced together from art (most of it from Carolingian Francia, not England, and much of that was inspired by classical art and hence is a little suspect on the details), language / vocabulary (ie, there's an Old English word for 'glove', so even though we've never found one we're pretty sure it existed), and a little bit of incredibly fragmented archaeology (scraps of garments that were recycled as boat caulking in viking Haithabu, scraps from graves in Sweden, etc - very little from England itself, again). So there's a lot of educated guesswork and gaps in our knowledge.

Building on what we know and can reasonably guess, there wasn't any kind of specialized rain clothing. It would technologically have been possible to make some kind of oiled or waxed fabric like 19th century sailors used to wear, but there's no evidence to suggest this was done. Instead, all the evidence that survives suggests that people wore a lot of wool, and linen on nicer occasions.

That might be enough, however, to keep you comfortable in all but the worst situations. Thick wool will keep the rain out for a long time, and it will keep you warm even once its wet. You'd still be uncomfortable if you spent a week camping in hard weather, but you'd say safe. And remember that even the Danish Great Army spent most of its time during the coldest times of year indoors, in large camps like the one currently being excavated at Torksey. Most Anglo-Saxons would have planned to be near shelter when the weather was rough.

So to the best of our knowledge, the answer is: wool, with a thick and possibly felted wool cloak over top to keep out the worst of the wet. And, in anything less than a full-on downpour, that would do a decent job (speaking from personal experience).

Edit: Also, good books! I especially enjoyed the most recent one :)