A narrow escape, a near miss. Both phrases are originally American. The first dates from the 1880s and is thought to come from sports, where a close call was a decision by an umpire or referee that could have gone either way. A close shave is from the early nineteenth century and reflects the narrow margin between smoothly shaved skin and a nasty cut from the razor. Both were transferred to mean any narrow escape from danger. Incidentally, a close shave was in much earlier days equated with miserliness. Erasmus’s 1523 collection of adages has it, “He shaves right to the quick,” meaning he makes the barber give him a very close shave so that he will not need another for some time. Two synonymous modern clichés are too close for comfort and too close to home.