This need not mean that to engage culture requires participation in the formal institutions designed to pass it on. Not at all. The disposition to develop and bequeath may take the form of performing work on oneself: reading, looking at art, listening to music in order to attune oneself imaginatively to the world in ways that will to make a difference on others (even if they may not.)
Engaging culture is to help imagination grow in what is, for Forster, its essential impersonality.
Forster's essay worries about what happens to culture thought like this in a society which tends to marginalize and disrespect the creative imagination and culture. His answer seems to be: if you do care about culture, hang in there and don't worry too much about the others, not even the State which is structurally anti-culture.
In this light, it is worth remembering Forster's advise that one of the best things you can do for culture is just to spend money on it.