Answering with the phone number was indeed much more common here in the past, and in fact at one time it was the method recommended by the G.P.O. and printed in the front "blurb" of the phone book.
Apart from being promoted as "good telephone manners" it also served the purpose of allowing coinphone users to hear that they'd reached the right number before pressing button "A" to deposit their money. Of course, those old phone are long gone now, and the money is gone the second the distant end answers.
When 2, 3, 4 and 5-digit numbers were commonplace it was easy to answer with just the number, or the exchange name and number for the shorter ones (mostly smaller villages). The 6-digit numbers were a little more of a mouthful, but still possible.
London and the handful of other large cities used 7-digit numbering, but up until the late 1960s the first three digits were dialed as letters representing the exchange name, so it was relatively easy to answer with "MAYfair 1234" or "WATerloo 5678." The change to All-Figure Numbering made it rather a mouthful to say "629-1234" or "928-5678," so the habit of just using the last four digits became common in these areas.