If you would rather that your piano tutor books aren't populated by elves, frogs and children's songs, no matter how charming, then here are one or two suggestions to be considered.
The Classic Piano Course by Carol Barratt, in 3 volumes, or an omnibus edition, published by Chester Music.
It's Never too Late to Learn by Pamela Wedgewood, puiblished by Faber Music.
Also worth considering is The Adult Piano Course published by Hal Leonard. This has a slant towards chords, and being an American publication, a good bit of American based music, but it gives one the chance to get to grips with one clef at a time!