The star 1SWASP J162842.31+101416.7 (WASP 1628+10) is one of several EL CVntype stars recently identified using the WASP database, i.e., an eclipsing binary star in which an A-type dwarf star (WASP 1628+10 A) eclipses the remnant of a disrupted red giant star (WASP 1628+10 B). We have measured the masses, radii and luminosities of the stars in WASP 1628+10 using photometry obtained in three bands (u', g', r') with the Ultracam instrument and medium-resolution spectroscopy. The properties of the remnant are well-matched by models for stars 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., we confirm that WASP 1628+10 B is a pre-He-WD. WASP 1628+10 A appears to be a normal A2 V star with a mass of 1.36 ± 0.05M ⊙ . By fitting models to the spectrum of this star around the Hγ line we find that it has an effective temperature T eff,A = 7500 ± 200 K and a metallicity [Fe/H] = −0.3±0.3. The mass of WASP 1628+10 B is only 0.135±0.02M ⊙ . The effective temperature of this pre-He-WD is approximately 9200 K. The Ultracam photometry of WASP 1628+10 shows variability at several frequencies around 40 cycles per day, which is typical for δ Sct-type pulsations often observed in early A-type stars like WASP 1628+10 A. We also observe frequencies near 114 cycles/day and 129 cycles/day, much higher than the frequencies normally seen in δ Sct stars. Additional photometry through the primary eclipse will be required to confirm that these higher frequencies are due to pulsations in WASP 1628+10 B. If confirmed, this would be only the second known example of a pre-He-WD showing high-frequency pulsations.