Next following

The sure sign of a lawyer who was soundly, but not sufficiently, beaten as a clerk.

I shan't give it to you William until the following day.

The “next following” day speaks to that nervousness that the day you have in mind — the one immediately following the one at hand — might not be the one your adversary does. For a day following this one might, conceivably, fall some indeterminate time — four days, eight days, who knows, even three hundred and fifty-seven days? — in the future. All days after this one “follow” this one; if you mean one cannot be sure it will be the one tomorrow.

This is the kind of argument you'd expect from that posh ginger girl on Just William.

“Violet-Elizabeth, can I have my rubber back please?”
“I shan’t.”
“But you said you would.”
“I most thertainly did not.”
“You said you’d give it to me on the following day.” “Tho I did. But not this following day. Another one. In Theptember, I shouldn't be thurprised.”

It pains me, readers, to think an adult learned in the ways of the law could be vexed by such a thought. Firstly, a following business day is not the same thing as the following business day. That definitive article restricts you to a single day.

But if you remain unsatiated; if you fear you may never see your india-rubber again, then use the word next.