In the light of yesterday's massive council by-election loss in Sunderland (not to mention another LibDem gain, winning control of Three Rivers District Council), it is not surprising that Labour is in no hurry to move the writ for a by-election in the Copeland constituency.
It would be possible for a party other than Labour to break with convention and move the writ. However, although as second-placed party at the general election, the Conservatives are best placed to take advantage of a Labour collapse, they may not want to risk losing face in the event that Labour hangs on. Likewise, there is no party advantage to Liberal Democrats, fourth in 2015, in pressing for an early election. UKIP, who were third, though ten thousand votes behind Labour, may feel they can take advantage of the situation. But who would want to be seen supporting a motion from the lone UKIP MP, Douglas Carswell? On the other hand, who would want to be seen voting against, especially as if it failed, the vacancy would remain unfilled for the rest of the parliamentary session. As someone remarked on Facebook, it would be a game of poker.
*Lincolnshire dialect for "frightened" as used by Margaret Thatcher of Neil Kinnock http://www.margaretthatcher.org/document/106812