http://www.englandfootballonline.com/teamplyrs/appsmost.html
It's an interesting one.
Terry Butcher is the closest to him with 7 captaincies in 77 appearances (Campbell had 3 in 73), in actual fact had Bryan Robson not got injured in the second game of World Cup 1990 Butcher would have ended up with just 3 captaincies himself too.
Tony Adams captained the side 15 times in 66 appearances which is the next closest, but he was club captain at Arsenal for donkeys, so that is still surprisingly low to me given that context.
Obviously a lot depends on who else is around at the time, but I'd suggest there's more behind this than race, although I really liked Campbell as a player.