Well, having consulted with my pillow and the internet, I have more.
Allium vineale is still very common across the whole of the South and South Midlands of England. So, it would have been easily found within reach of anywhere in Alfred's realm.
A study has been done on Alabama crow garlic that must have been introduced from the Old World. The oil has 5.2-6.5% of the non-sulphur compound p-vinylguaiacol. 99.3 % of garlic oils are sulphur compounds, 91.6% of A.v. oils. They have many similar sulphur compounds but different compounds in each are at the higher percentages.
p-Vinylguaiacol (related structurally to vanillin) contributes to the aroma of buckwheat and some wheat beers and has been described as "spicy powdery clove phenolic woody smoky balsamic amber". Phenols can be antibacterial, though I can't find any mention for this one yet. There are a lot of brewing research papers. Thymol and carvacrol are potent antibacterial and antivirals that are even active against norovirus. The vinyl part of the molecule is quite reactive, so it might be changed after days in the medicinal mixture.
Prabodh Satyal et al "The Chemical Compositions of the Volatile Oils of Garlic (Allium sativum) and Wild Garlic (Allium vineale)" foods (2017) 6:63 The journal is called "foods" and I am not sure how to do italics or bold with this.
DUDE that's so amazing! Your internet skills are amazing. Honestly I have nothing to add to this, but thank you so much for sharing what you found!