No announcement has been found in English Mechanic v. 25:
the reason is probably that the relevant page is missing from the
source used. The most likely page(s) is: 25/635 (1877-05-25), p. 271-272,
as it is the last lacuna before reports of received sets were published.
The best guess as to the requirements, based on the reported awards, is
single set of 3x#2-4, with one prize for
the best set, and three prizes for the best #2, #3 and #4 problem.
Based on the reports of received sets, seven composers competed. It is worth noting that one of the judges (J. P. Taylor) won two of the prizes.
A solution tourney appears to have been held for published tourney problems.
Shortly after the awards had been presented, J. P. Taylor resigned his prize as he didn't think a competitor should receive two prizes. Instead he wished it to be awarded to the composer of the set Gang forward, provided that this composer became a member of the British Chess Problem Association.
This seems odd: while J. P. Taylor, as a competitor, may resign or refuse his prize, it is not clear that he, in that role, can prescribe who shall receive it instead, and especially not require the recipient to become member of the B.C.P.A. in order to receive it. His second role, as #2 judge, does not seem to extend to awards for full sets.
The tourney manager may have considered accepting this suggestion / condition, as a request for the name of the composer of Gang forward was printed, but this may easily be for other reasons. As no direct announcement has been found that the composer, G. J. Slater, was awarded the main prize, no changes have been made in the original list of awards.
A possible complication to the proposed change is that one of the problems in the set Gang forward was identified to be faulty on publication the week before the awards were published. The fault was described as a dual solution, but as printed it is a mate-in-one, suggesting that it probably has been misprinted. No corrections have been found so far.
Locate the missing announcement.
Prize best set: J. P. Taylor
Key: 1. Na6
Source: English Mechanic, 26/658 (1877-11-02), p. 202, prb. 392
Key: 1. Ra7
Source: English Mechanic, 26/658 (1877-11-02), p. 202, prb. 393