The star 1SWASP J024743.37-251549.2 was recently discovered to be a binary star in which an A-type dwarf star eclipses the remnant of a disrupted red giant star (WASP 0247-25 B). The remnant is in a rarely observed state evolving to higher effective temperatures at nearly constant luminosity prior to becoming a very low mass white dwarf composed almost entirely of helium, i.e. it is a pre-helium white dwarf (pre-He-WD). We have used the photometric database from theWide Angle Search for Planets (WASP) to find 17 eclipsing binary stars with orbital periods P = 0.7-2.2 d with similar light curves to 1SWASP J024743.37-251549.2. The only star in this group previously identified as a variable star is the brightest one, EL CVn, which we adopt as the prototype for this class of eclipsing binary star. The characteristic light curves of EL CVn-type stars show a total eclipse by an A-type dwarf star of a smaller, hotter star and a secondary eclipse of comparable depth to the primary eclipse. We have used new spectroscopic observations for six of these systems to confirm that the companions to the A-type stars in these binaries have very low masses (≈0.2M⊙). This includes the companion to EL CVn which was not previously known to be a pre-He-WD. EL CVn-type binary star systems will enable us to study the formation of very low mass white dwarfs in great detail, particularly in those cases where the pre-He-WD star shows non-radial pulsations similar to those recently discovered in WASP0247-25 B.