I play tunes rather than songs(I only sing in the bath!)My repertoire is mostly traditional (English, Scottish, Irish, and a few Welsh) but I do include some great 'composed' tunes that do not feel out of place - including lots by James Scott Skinner, Tom Anderson, and a few by Ric Sanders, and Chris Newman.
BTW would people regard tunes by Carolan, or James Hill, say, are traditional, or composed?