It's a highly context-specific allusion to the fact that there had already been at least one by-election in the North of England recently (the story was written around 1914). This isn't explicitly stated earlier in the story, but it's strongly implied by the preceding paragraph which makes many references to political unrest.
Most likely the speaker represents or endorses the current ruling class, which is why he says By-elections are not very desirable at present (since he and/or his allies are currently in power, they'd rather keep it that way and not risk losing control "bit-by-bit" through by-elections).
And certainly the readers of the time would know all about Britain 1911-1914: The great unrest.
Compare...
1: Do you want a slap?
2: Do you want another slap? (by implication, in addition to the slap/s you've already had)