The British authors and teachers of Philosophy  Helen Beebee, Nikk Effingham and Philip Goff wrote in his book «Metaphysics»:

«Phenomenalism and idealism are closely related philosophical positions and basically amount to the view that the external world (and the familiar objects that populate it - trees, cars, bananas and so on) is really no more than a collection of sensations or experiences or sense data. As George Berkeley put it, "esse es percipi" or "to be is to be perceived". Phenomenalism and Idealism are both version of anti-realism(...); because on both views the existence and nature of the external world are mind-dependent (indeed the external world are mind-dependent (indeed the external world just is mental, it is just a collection of sensations).»(Helen Beebee, Nikk Effingham and PhilipGoff, Metaphysics, The Key Concepts, pages 162, Routledge, London and New York, 2011; the bold is put by me).

It is true that for idealism the external world just is mental but that is not a correct definition  for phenomenalism as a hole. Phenomenalism is not, necessarily, anti-realism. There can exist four versions of phenomenalism: idealistic (like Hume, Kant), realistic, phenomenological, skeptical. What is phenomenalism? It is empiricism: the view that we only know the phenomena, the objects as they appear to us, the data-sense, and that we can only infer, by metaphysical intuition, in a vague way, the nature of what is behind the phemonena (an unknown matter, as realism says; a spiritual world or nothing, as idealism sostains; something unknown, as skepticism).

Why was David Hume an idealistic phenomenalist?  Because he sostained that the permanence of the objects and their matter were ideas of our imagination, and not realities in themselves. However, no author of analitical philosophy classifies Hume as an idealist: they don´t have a clear vision of ontognosiology. Idealism is beyond empiricism, on the ontological plan. And Kant was also an idealistic phenomenalist: he maintaind that we only know the phenomena (for example: houses, dogs. cities, humans bodies), which are creations in our external mind (the space), and that the real objects are the the noumenon, metaphysical beings outside of space and time, that is, outside the sensibility of each person (noumenon : God, Soul, Freedom).

«Phenomenalists and idealists do not want to deny obvious facts such as the fact that my feet still exist when I am asleep, and the difference between them comes to exactly how they account for those facts. Idealism - the position advocated by Berkeley -  appeals to the existence of God: you might not feel your feet when you are asleep, but God is all-seeing, and he perceives your feet, thus ensuring their continued existence.»(...)

«Phenomenalism makes no such appeal to God. On the phenomenalist view an object is (as J.S.Mill put it) a "permanent possibility of sensation».

  (Helen Beebee, Nikk Effingham and Philip Goff , Metaphysics, The Key Concepts, pages 163, Routledge, London and New York, 2011)

It is an error to assure that « phenomenalists and idealists do not want to deny obvious facts such as the fact that my feet still exist when I am asleep». In fact, the phenomenalist David Hume has doubts about the existence of our feet when we are sleeping, since the notion of permanence resides in us, in our mind, and not in the problematic external world, including our body. Of course some idealists and phenomenalists guarantee the invariably permanence of our feet organically linked to body while sleeping,  but not all support this opinion.

Another error of this text above is to postulate that «Idealism - the position advocated by Berkeley -  appeals to the existence of God». Some kind of idealistic Buddhism holds that the world is illusion and there is only my spirit and need not conceive of God. Even Descartes, when formulating the reasoning «I think therefore I am», plunges into solipsistic idealism without needing the existence of God.

«The phenomenalist denies that there is any distinction between the way the world is and the way our experiences represents it as being.»(Helen Beebee, Nikk Effingham and Philip Goff , Metaphysics, The Key Concepts, pages 165, Routledge, London and New York, 2011).

This is a falsehood. All phenomenalists distinguish between the sensa-data, the way they perceive the problematic external world, and the partially or totally ignored constitution of these last. For example, Kant, a phenomenalist, distinguish between phenomena and noumenon, the unknown reality. Only the naive realism identify the content of the external world and the content of empirical perception of it.

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