Can someone identify this piano piece for me?

In the 1985 Merchant Ivory Productions version of A Room with a View, Lucy Honeychurch plays Schumann (?) at “Mrs. Vyse’s well-appointed flat” for guests. Can anyone tell me more about this tune?

Go to 1:15 to hear it.

I’ve tried looking this up before, to no avail. If someone can recognize it, please let me know.