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The ability to move through check to capture the enemy Queen is the power
that keeps Queens from being able to check each other. On an otherwise
empty board, suppose that White has a Queen at e1 and a Rook at b1, while
Black has a Queen at a9. If Queens did not have the ability to move
through check to capture an enemy Queen, then White could check the Black
Queen by moving the White Queen to e9. Since the Rook would impair the
Black Queen's ability to move over b9, the White Queen could freely pass
over it to a9. So the White Queen could check the Black Queen without
being in check from it. But as the rules of British Chess stand, the move
of 'Q e1-e9' would put both Queens in mutual check and be illegal. It
would be mutual check because of the Queen's ability to pass over checked
squares on a move to capture the enemy Queen. Such a move would never
actually happen, because the preconditions for it are illegal, and those
preconditions are made illegal by the Queen's power to otherwise make
such a move.

In Chess, pieces have the power to capture the enemy King, and the only
reason they don't is that it is illegal for a player to keep his King in
a position it could be captured from, and when this can't be done, the
game ends before the capture can be made. The same is true for capturing
Queens in British Chess. Queens have the power to capture each other, but
there will never come a time in the game when one can use that power to
capture the other. This power affects the game only through the
restrictions it puts on the movement of Queens. The restrictions that
follows from this power is that Queens may never face each other across
any empty orthogonal or diagonal line of movement, and restrictions on a
Queen's movement never restrict its power to restrict which spaces the
opposing Queen may pass over. So, in the example I gave, it would be
illegal for the White Queen to move from e1 to e10, because that move
would pass over e9, which is covered by the Black Queen.