What is the meaning of "let in" in : "but they were let in in early in the spring through the Venezuelan loan, as no doubt you remember"
In this story, Coxon & Woodhouse was a firm of stockbrokers or similar financial business. Doyle implies that it was involved in the finances of a loan associated with Venezuela. Doyle uses "Venezuelan loan" as a fictional proxy for a real-life large loan associated with some distant (and in those days, either by implication or by public knowledge, risky) national business. The consequence of involvement in such a loan, risky and probably fraudulent, ruined Coxon & Woodhouse.
The firm was "let in" in the sense of:
"let in" = to involve or commit unfavorably
"the provisions … could still let us in for trouble" — Elmer Davis
" ... smiled at all her schemes, little dreaming that … she was letting him in for some £20,000"
Merriam Webster