There are very obviously algorithms in P which are not "efficient". For example, an algorithm in O(n^10^10^10) is not efficient in any reasonable sense. It is in fact much much much less efficient than O(e^n) for any n low enough that the whole thing would finish in under a year or so.
In practical terms, the class of efficient algorithms is probably O(n^3) at best, and even then assuming no huge constant factors.
In practical terms, the class of efficient algorithms is probably O(n^3) at best, and even then assuming no huge constant factors.