Perfectly normal at our A/G field to call G-XX, Downwind, Contact 1 Ahead, contact 2 ahead etc. Just lets the other pilots know you have seen them.
You can go even further, G-XX, Downwind for runway 07, Contact 1 ahead.
It's just common sense really if it helps other people, if I'm turning base and someone calls just 'Downwind' it's OK, if they call Downwind Contact 1 ahead and I can't see anyone else I can be reassured they have probably seen me.
PS I don't see this has any bearing on an ATC unit which would be number 1 to land number 2 land, and ATC would be informing the pilot of that situation not the other way around, at an A/G field a lot of the time your information is direct to other pilots in the circuit, not a 'controller'.