I happen to know that the aircraft on final was a pre solo student with an experienced instructor practicing flapless circuits. The students calls may have been late but would have been made and a final call was made after the ready for departure call - so you must have missed this. The student would be instructed to go around at 300ft if the runway is not clear.
No big deal though - we all make mistakes, sometimes we fail to see aircraft on approach (especially when they are lower than you expect to see them - flapless - or perhaps higher as in glide approaches), it is a training airfield with lots of non standard/normal approaches. But you made your calls and the student made a safe and timely go-around.
Just a note on A/G radio. There is no requirement for response to any calls other than those requesting airfield information. All other calls are effectively made blind and are for the purposes of other pilots in the facinity of the airfield. If other A/G airfields choose to respond to such calls that's up to them but is not a requirement. Everything is at the pilots discretion and hense all the more important that we all use our eyes and ears. I know this is disconcerting to those more used to controlled airfields but its all part of aviations rich tapistry.