In this instance, “ledge the bants” is code for “lick the butts”, so that it doesn’t look so dubious when Ed receives emails from his boss along the lines of:
“Ed, those guys down at the Royal Albert Hall aren’t yet sure about our bus dev proposal to make them a club with nothing but all-night long Dixon sets - how ’bout you go over there and give those bants a good ledging, see if that doesn’t convince them!”.