I've been looking at these for @instituteforgov since it last looked like this might happen. Here's a short thread with five quick insights from historical no-confidence motions:
The last confidence motion we had was in November 1994, and the last time the opposition tabled a motion of no confidence was in March 1991.
15/24 successful no-confidence motions were tabled against minority governments.
Each administration kept the confidence of its party, but lost the support of the House (though remarkably MacDonald won over 12 Liberals and 2 Conservatives).
During the winter of 1978-9, Thatcher was under extraordinary pressure to no-confidence Callaghan's Government, but only tabled a motion in March 1979 after the SNP had already done so.
According to Phillip Norton, the motion of no confidence against Callaghan was the only one in the twentieth century where the outcome was unclear until it was announced.