This actually, of all things, a question based in the books series A Song of Ice and Fire. There's a character named Craster who lives in an analog of Northumberland/Southern Scotland in those time periods and he is described as drinking a "thin yellow beer" which I can't identify. I'm curious if this description would line up with any real kind of beer making from these time periods in these areas. It's a tough question for a bunch of my fellow fiction nerds to answer as we're knowledgeable on mostly made up things, was hoping this community would have a better shot at answering this.
In that time frame the English would have been brewing Ales and Beer. While today, ale is considered a form of beer, back then there was a difference. Beer incorporated Hops, Ales didn't.
Beer isn't terribly hard to make, it is really only four ingredients, Malted Barely, Water, Yeast and Hops. All of this would have been readily available, though the yeast strains probably wouldn't have been as refined and could have been introduced naturally via wild yeast, though this would take away a bit of the control of the brew.
The process would have been much like today where the Malted grains are mashed with water around 160 degrees and then Sparged (drained) into a boil kettle. However, today, a brewer with do multiple sparges into the kettle to get as much fermentable sugar into the wort as possible. Back then, they still would have done multiple sparges, but would have used it to make seperate batches. The first sparge would contain the most sugar, and would therefore lead to a better and higher alcohol level. The second and third sparges would have had dramatically less sugar and created a low alcohol brew that would have been used for every day drinking. This low alcohol brew would have to be consumed very soon after fermentation completed as it would spoil quickly, especially if not hopped.
I am not a historian, but have dabbled quite a bit in homebrewing, so I hope this is ok.
Here is a source that goes into the process and even provides a recipe to recreate a medieval beer using modern ingredients.