Sepsis, typically caused by septicaemia or blood poisoning from infected wounds, still kills on average 37,000 people annually in British hospitals (UK Sepsis Trust 2015) and around 270,000 Americans (CDC, 2019) every year, so even with all of our modern medical knowledge, technology and pharmaceuticals, an infected cut can still kill you. An early medieval English Leech might not have understood modern germ theory, but he still would have understood that a dirty wound gets infected and that an infection can kill you. A source I return to again and again is Bald's Leechbook, a 9th Century English medical textbook commissioned by a man called Bald, presumably a leech or doctor. The Leechbook is a fascinating combination of Classical medicine and contemporary treatments and herbolgy, much of which is actually rooted in evidence-based medical science.

The Leechbook contains essentially a whole chapter dedicated to:

Treatments and wound salves and drinks for all wounds and cleansings in every manner

The majority of these treatments require herbal remedies, but a central component of all of them is either that everything is boiled together, or added to hot wine; while these practitioners may not have understood the concept of sterilisation, they clearly understood that wounds washed in boiled water or alcohol were much less likely to be infected. A common herbal component is sage, which is known for having some antimicrobial properties.

Anglo-Saxon medicine is big on topical treatments, salves and washes. Many of the salves and washes listed in the Leechbook contain herbs still used today (albeit in clinically refined form) as anti-inflammatories, analgesics or anti-fever medications, and it even contains a primitive coagulant to try and stop hemorrhaging wounds. A small wound or scratch could be treated with warm, clean honey (again known for antiseptic properties) or:

If you want to quickly treat a small wound, triturate watercress or boil in butter, make into a salve, smear with.

It's likely that the washing with boiled water is the most important part of this treatment. In the event that the wound gets infected, the Leechbook suggests washing it with hot wine, cutting away dead flesh and binding with honey. There are treatments even as far as amputation of infected and gangrenous limbs:

If you want to cut or amputate a limb from the body then examine which that place is, and the function of the place, because if one carelessly treats that place some quickly rot, some feel the treatment later, some sooner. If you should cut or amputate an unhealthy limb from a healthy body then you cut at the limit of the healthy body, but much more cut or amputate on the healthy and living body so that you may better and sooner heal it.

The Leechbook also illustrated the importance of quickly and effectively cauterising a hard to clean wound, like an animal bite, to prevent infection setting in:

When you set fire upon a person then you take pond-leek’s leaf and ground salt, cover the place, then by that the heat of the fire is sooner taken away. That is useful for the bite of a botrax or a dog, if one does it immediately, and again for three nights smear with honey so that the scab may fall off more quickly.