You could try this function:
letter2number <- function(x) {utf8ToInt(x) - utf8ToInt("a") + 1L}
Here's a short test:
letter2number("e")
#[1] 5
set.seed(123)
myletters <- letters[sample(26,8)]
#[1] "h" "t" "j" "u" "w" "a" "k" "q"
unname(sapply(myletters, letter2number))
#[1] 8 20 10 21 23 1 11 17
The function calculates the utf8 code of the letter that it is passed to, subtracts from this value the utf8 code of the letter "a" and adds to this value the number one to ensure that R's indexing convention is observed, according to which the numbering of the letters starts at 1, and not at 0.
The code works because the numeric sequence of the utf8 codes representing letters respects the alphabetic order.
For capital letters you could use, accordingly,
LETTER2num <- function(x) {utf8ToInt(x) - utf8ToInt("A") + 1L}