That's a nice archaeological find. However, I'm not so sure there is in fact a checkmate in just one "move". Of course, there is a (unique!) checkmate for both colors in all orientations considered by @Brian Towers, which makes this a very nice problem indeed. But what about the other orientations?
You may protest that there's a rule that the bottom right corner must be a light square, but I think you're going to have to consult a historian to determine whether this rule was in effect in this particular late 19th century London chess club, and in particular whether the game could have continued without rotating the board if the players noticed their error during the game. You likely also need to consult a medium in order to determine whether one of the players noticed it. So, I think this rule doesn't mean we can exclude other orientations.
You may argue that the other orientations are excluded because there's a pawn on the side of the board. Not quite. First, a pawn can never legally be put on the first rank, so that excludes one orientation (white being to the left of our current view). But this is not true for the eighth rank. Promotion of a pawn is done by first moving the pawn to the promotion square on the eighth rank, and then replacing it with another piece. So, it is possible for a pawn to be on the eighth rank in a legal game. Of course, in the current state of the board the move is not yet completed, but that doesn't matter. We already know that in the other orientations the game was ended before the checkmate (as we still have to make one move), so the same could happen in the middle of the promotion move. I certainly have seen the board being left abandoned in such a state at my own chess club.
It could be possible that we can show the position is unreachable via retrograde analysis, but that seems very difficult, so I'm just going to leave that to others and just say that I don't know how to prove this one way or the other.
Ok. So, let's assume the pawn on the side from our orientation is mid-promotion. Now suppose white wanted to promote into a knight. This is check, but not checkmate, as black can take the knight with the bishop. However, black cannot give mate here while getting out of check at the same time. So, neither player can give checkmate in one move. (technically, I have shown this is not possible in one half-move, but I believe the technical term "Mate in one" is generally understood to refer to one half-move)
In conclusion, I believe I have made a decent argument for why there exists a scenario where this position has been reached from a perfectly legal game (under the rules in this particular chess club), yet there exists no mate in one. Hence, however unlikely my scenario may be, I must conclude that I cannot be certain that there is checkmate in one move.
That said, I don't think my problem hurts the essence of your
archaeological find clever composition. As long as the promoted piece can deliver checkmate as well, we can be certain that there is a mate within one move.
I think just placing a pawn between the bishop and the pedantic promotion square would do:
[title "Mate in one"]
[FEN "3b4/R3P3/1pkPR1n1/P1p1n3/4K1p1/2Nr4/5p2/1b6 w - - 0 1"]
I believe this does not change the checkmate moves in the other orientations, or even their uniqueness. It does make the checkmate for white easier to find in the other orientations, but I think the new orientation you get in return is more than worth it. Maybe there are retrograde arguments against this position, I'm not sure.