OED says that:
Middle English buryel, biriel, incorrectly formed as a singular of byriels, buriels n., q.v.; in later times associated with nouns in -al from French, such as espousal-s.
Etymonline.com says that:
“act of burying,” late 13c.; earlier “tomb” (c. 1200), false singular from Old English byrgels “tomb,” from byrgan “to bury” + suffix -els;
How is the word burial incorrectly formed? What would be the correct form if it wasn’t incorrectly formed?
According to OED, buriels was used but it is obsolete now.
Here is the etymology of buriels from OED:
Old English byrgels strong masculine, cognate with Old Saxon burgisli neuter, < burg- ablaut-stem of bergan bergh n. to protect + suffix -isli– ; compare Old English græfels quarry, fætels purse, etc.
The answer is in the OED‘s definition of buriels1, namely
A burying-place; a sepulchre, tomb.
An interment, funeral.
Note that both meanings are already singular: A burying-place, An interment, etc.
So the “correct” formation of burial would be buriels. It was “falsely” constructed because the singular, Old English word was mistakenly believed to be a plural, French word. From the OED’s etymology of burial (just after the part you cited):
in later times associated with nouns in -al from French, such as espousal-s.
1 “ˈburiels, n.” OED Online, Oxford University Press, June 2017, www.oed.com/view/Entry/24975. The etymology of buriels is helpful in pointing out how a singular English word ended up ending in -s (among other things). Note that the OED Online is unfortunately a prescription service (behind a paywall). However, many folks, especially in the UK, will have access through their local public library, and most students should be able to access through their institution’s library. More info here: http://public.oed.com/about/free-oed/
2 “burial, n.” OED Online, Oxford University Press, June 2017, www.oed.com/view/Entry/24969.