Per advert in The Family Herald
https://catalog.hathitrust.org/Record/012304787 v.3, p.368:

HOME, HOME! SWEET HOME!

Those who wish to make Home happy, and the Evenings pass joyfully and pleasant, should purchase No. l of the TOM THUMB SONGSTER, wherein they will find, for One Penny, above Eighty of the most Popular Songs extant, selected with care, and suited both for Home and Public use. In addition to the above will be found a neatly engraved Portrait of SWEENY, the popular Banjo-player, and many Songs as sung by him and the much-admired Virginia Melodist at all the principal Theatres.
London: Office, l, Shoe Lane ; and may be had of all Booksellers in any part of the globe

Per advert in The Sportsman's Magazine
http://catalog.hathitrust.org/Record/008917227 p.274:

Now ready, No. 1 to 8, price one penny each,

TOM THUMB SONGSTER.
Each No. contains nearly sixty songs. No. 1 contains a Portrait of Sweeny, the Banjo player. No. 6 contains a Portrait and fourteen Songs of that much admired and popular songstress, Miss Eliza Cook, (by permission). No. 7 a Portrait and seven Songs of Mr. S. Cowell, of the Theatre Royal, Surrey. No. 8 contains seven Songs by Miss Lalldon (L. E. L.), and eight Songs from the Opera of Maritana. No. 9 will contain Russell's popular song, the Dream of the Reveller, and sixty others. A No. of this Songster is published the 27th of each month.

and also at p.526:

FOURTEEN SONGS BY ELIZA COOK.

No. 6, of the TOM THUMB SONGSTER,
Price One Penny, Contains the following Songs
Thirteen of which are by the above-named Popular Writer, together with a beautiful Portrait.
The Old Arm Chair
The Heart, the Heart
The Old Water Mill
Trouble your Heads with your own Affairs
I miss Thee Mother
The Old Clock
The Poor Irish Boy
Song of the Modern Time
Song of the Haymakers
Manly Love
Summer is Nigh
Teddy O'Neale
Love On
Ode on Burns
>
>
And Twenty-three other Popular Songs.
Remember No. 6, Fourteen Songs, and Portrait of Eliza Cook.
The Nos 1 to 5 are constantly on sale. No. 7 will be published January 27, 1846.
London: Cleave, Shoe Lane; Purkess, Compton-street, Soho; Hey wood, Manchester; Guest, Birmingham; France, Newcastle; Myers and Shepherd, Liverpool; Love, Glasgow; and all Booksellers.

Per advert in The London Journal (and Weekly Record of Literature, ... ) for the week ending May 9, 1946
https://books.google.com/books?id=nHs-AQAAMAAJ&pg=PA160 p.160

SONGS TO SUIT EVERY BODY, BOTH PRIVATE AND PUBLIC.
Now ready, Nos. 1 to 10, price one Penny each, containing nearly sixty songs in each number, sixty-four pages of good clear type, printed on good paper, and enclosed in an ornamental wrapper, the TOM THUMB SONGSTER.
No. 6 of this popular song-book contains a Portrait, and fourteen of the best songs, of MISS ELIZA COOK (by permission). No.8 contains seven songs by Miss Landon, and thirty others. No. 10 contains correct likenesses of the Ethiopian serenaders, as they appeared at St. James's Theatre: the popular songs of Old Dan Tucker, Old Tar River, Down among the Dead Men, the songs from the opera of Norma, and forty others.
Volume I of the above is just published, in a neat ornamental binding, price One Shilling.