Obviously, if you can find real, fresh epazote at a local spice vendor's, go get it, it's a lovely herb. It is definitely not an herb that I would recommend bothering to substitute if you have access to the thing-in-itself (unlike, say, cassia and true cinnamon, or fennel seeds and anise; nothing in my experience is close to epazote, and so epazote cannot truly be substituted).
But since the point of this question is to do that anyway, the main flavor-purpose of epazote is to provide a sharp flavor (that's the part described as "medicinal", or "like creosote") with "smoky", "bitter" undertones. The reason the recipe mentions "a sprig" is because epazote is intensely flavored but loses that flavor quickly under heat, and so is typically added at the end; the small amount is sufficient to permeate the soup with flavor.
The site above records, supposedly from a comment on a page somewhere at the University of Graz, though the link is dead, "a mixture of savory, oregano and boldo leaves". Sadly, I've never tried boldo, though, and cannot attest to what herb would replace it. I also don't know if it's available in England, knowing only that it is Peruvian-native.
For a personal recommendation, boiled pine needle is the closest analogue for the sharp part in my experience; if you have access to pine needles (I've heard Scots pine is native to Britain, be careful of impostor junipers), don't be shy about washing some gathered needles and steeping them like tea (the sharp scent of pine mellows out with boiling into something akin to epazote).
Juniper berries have the same flavor, but juniper is toxic in high amounts, unlike the needles of other conifers; so I have never used it. Also, it makes sense that a food with a flavor described as "like creosote" would also be similar in flavor to boiled pine, since a major source of creosote is pine tar, made from pine wood fired oxygen-free.
My recommendation based on personal experience would therefore be to just add the pinewater right to the soup, together with oregano, thyme, rosemary, and a dash of cumin since all those herbs have resinous, "bitter" notes for the undertones.
...lastly, since, realistically, you're probably not going to be using pine needles either, I would recommend combining these two separate recommendations; some combination of summer savory, oregano, thyme, and perhaps mint, cilantro, or lemon zest for extra sharpness. It won't be epazote, but it should fill the role similarly.