There's a Dorothy Hewett poem, Sailor Home From The Sea, set to music by Chris Kempster, very popular in the Australian folk clubs & festivals, starts out, O cock of the morning/With a dream in his hand, and you have to remember not to start, O dream of the morning, instead.

I once started singing a set of lyrics to the tune of a different song, realized what I was doing, but couldn't for the life of me remember how the correct tune went, so I sang the whole song through to the wrong tune.

I think it may have been Queen Elinor's Confession, to the tune of An Irish Song (by Ed McCurdy). Or maybe it was the other way around.