So I get both chargers out and set them up to charge. I plugged the MH-25a (supplied with the D810) in and inserted a battery and although it charges, there is a loud sparking noise coming from it and a nice smell of burning electronics.
Luckily, the D810 and D7100 both use the same EN-EL15 Battery so the MH-25 charger that comes with the D7100 (notice the “a” missing, I’m led to believe it just has a slightly lower power output) can charge all 4 batteries.
So a big thanks to Nikon for standardising their batteries throughout their range. I’ll give Wex Photographic a call to get this charger sent off for repair/replacement.