This related to the EI Saver Fare which is the base fare which does not include a seat allocation.

There is a curious HBO fare on BA, as in hand baggage only which is the lowest fare but thats kind of opposite to this.

In simple terms if the ticket number does not start with 053 you always have 10kg carry on. If it starts with 053 the rules above apply which allow for a very broad range of passengers to carry on onboard