They looked at the law, saw “motor vehicle” and said that an ox cart doesn’t have a motor so should be fine.

> Oxford’s congestion charge is almost certainly enforced by cameras that scan your number plate. An ox-drawn cart doesn’t have a number plate, so it won’t be charged. Other vehicles like a Renault Twizy or Reliant Robin do have number plates, so they’ll be charged even though they’re technically exempt.

So there's not much to it: Plates are scanned -> the number is checked in the vehicle registration database -> not class M1(a) or class M1(b) -> no charge.

This goes for ox carts, Twizys and Reliant Robins.