It's the tale of a woodmouse--the titular Mrs. T--who finds numerous uninvited guests mucking up her tidy home in a hole under a hedge. The interlopers--mostly bugs of various sorts, though also a bloated, inconsiderate frog--make all manner of ruckus, demanding food and/or shelter and leaving footprints all over her well-kept home. Eventually she expurgates them all and spends an entire fortnight cleaning and securing her domicile against future invasion. Once she's accomplished this feat she throws a party for her other mouse friends, which the frog attempts to crash with only partial success.
The comparison with Thorin and company is obvious, but it's really the description of the house itself that is most evocative of Bilbo's home, describing the tidiness and vast number and purpose of rooms littered throughout the subterranean passages. Significantly, her home is described as sandy, something which Bilbo's hole full of larders and parlours and pantries was described as most certainly not being. Also, her description of the spider seems like it might have had an influence on the malevolent rendering arachnids received in Tolkien's work.
The book was published 27 years prior to the publication of The Hobbit. Seeing as Tolkien fathered several children in the intervening years, and since this was probably the only children's book available in England back then--besides the other 400 books in Potter's catalog; apparently she was the Dr. Seuss of the pre-war era--it seems entirely unlikely that Tolkien was not intimately familiar with this story. Maybe the academics have already chewed this connection to pieces, but if not, here's a freebie to any student of 20th Century British Literature looking for a thesis topic. You can thank me in cash or money order.