People didn't always say pea or newt. These seven words initially started as other words entirely.
Originally the word was pease, and it was singular. ("The Scottish or tufted Pease ... is a good white Pease fit to be eaten.") The sound on the end was reanalyzed as a plural s marker, and at the end of the 17th century people started talking about one pea. The older form lives on in the nursery rhyme "Pease-porridge hot, pease-porridge cold …"
The same thing happened to cherise or cheris, which came from Old French cherise and was reanalyzed as a plural. So the singular cherry was born.
Apron also came into English from Old French and was originally napron. ("With hir napron feir .. She wypid sofft hir eyen.") But "a napron" was misheard often enough as "an apron" that by the 1600s the n was dropped.
Umpire lost its n from the same sort of confusion. It came to English from the Middle French nonper, meaning "without peer; peerless." ("Maked I not a louedaye bytwene god and mankynde, and chese a mayde to be nompere, to put the quarel at ende?") A nompere or an ompere? The n-less form won out.
The confusion about which word the n belonged to could end up swinging the other way too. A newt was originally an ewt ("The carcases of snakes, ewts, and other serpents" is mentioned in 1584's The Discoverie of Witchcraft), but "an ewt" could easily be misheard as "a newt," and in this case, the n left the "an" and stuck to the the newt.
The n also traveled over from the "an" to stick to nickname, which was originally ekename, meaning "added name."
Alligator came to English from the Spanish explorers who first encountered el lagarto ("lizard") in the New World. While the big lizards were for a time referred to as lagartos, the el accompanied often enough that it became an inseparable part of the English word.
All example quotes come from the Oxford English Dictionary.
This list first ran in 2013.