Daniel,
This works reasonably well on the few that I tried. Will likely need adjusting if the format is different in some of the transcripts. Also does not remove footnote numbers from the text. Will have to parse the HTML to do that.
brixtonLetter[number_] := Module[{plaintext, start, end},
plaintext =
Import["https://russell-letters.mcmaster.ca/brixton-letter-" <> ToString@number, "Plaintext"];
start = StringPosition[plaintext, "Original"][[1, 2]] + 2;
end = StringPosition[plaintext, "Notes"][[1, 1]] - 1;
StringTake[plaintext, {start, end}]
]
To get the transcript for letter 20
brixtonLetter[20]