Another Alice Book, Please! by A.L.Gibson.
Published by John Castle in 1924. Hardback, no dust jacket.
Very pretty black and white illustrations by H.R.Millar.
An Alice-like fantasy written at the request of the author’s children who wanted more “Alice”.
I can’t find much info on the author, but the illustrator was a well known artist of children’s literature from the late 1800s to the early 1900s, including some of the coloured Fairy Books (which I loved as a kid). He also worked with E. Nesbit, illustrating Five Children and It and The Phoenix and the Carpet. There’s a full list here.
On amazon: Another Alice Book, Please!
Alice in the Internet 
Years later the author revised the book quite extensively and published it as “The Tail Tale”. I think the original is much better.
It’s amazing just how many Alice’s there have been. Does anything else rival it for ‘new versions’?
Ack: I mean Alices, not Alice’s.
I know the name of the illustrator, he is H.R. Millar