Lost in Blunderland by Caroline Lewis.
Illustrated by S.R.
Published by William Heinemann, 1903.
Sequel to Clara in Blunderland.
Written by Harold Begbie and J. Stafford Ransome under the pseudonym of Caroline Lewis. This reversal of Lewis Carroll’s name is pleasing to me, as his pseudonym was originally chosen by taking Dodgson’s first names (Charles Lutwidge), reversing and ‘latinising’ them to Ludovicus Carolus, and then re-Englishising them again.
As with the first book, the illustrations are credited to S.R., and I believe they were the work of the J. Stafford Ransome part of the partnership, and again they echo the Tenniels, but look like genuine political caricatures. Clara herself is Balfour.
I bought this from Stella and Rose Books. You can buy a modern reprint here.
On amazon: Blunderland
Alice in the Internet 
You’re welcome to display the cover of the modern reprint if you wish.
Oh, and the introduction to the Evertype edition has photos and short bios of the main characters, to help put the 1903 political caricatures into context.
Oh, cool- thanks. I’m fairly clueless about who is who in most of my political Alices…