Here's another book that is viewable online (at least in the US):

The Songs of Charles Dibdin, Chronologically Arranged, with Notes, Historical, Biographical, and Critical; and the Music of the Best and Most Popular of the Melodies, with new Piano-Forte Accompaniments

Vol. I. (London: How & Parsons, 1842). - None of the songs in this volume have musical notation.

Vol II. (London: G. H. Davidson, 1848). – Some songs have music.

SONGS TO WHICH THE MUSIC IS GIVEN.

TITLE. - FIRST LINE.
A Little - Wid mi Lor' Anglois I came over un valet
Advice - Old Mary, her poor husband dead
All Girls - No more of waves and winds the spurt
All's One to Jack - Though mountains high the billows roll
Anna, Anne, Nan, Nance, or Nancy - My love's a vessel trim and gay
Anne Hatheawaye - Would ye be taughte, ye feather'd thronge
Bottom; or, Tol de Rol - Of all the lives that e'er was liv'd
Broken Gold - Two real lovers, with one heart
Captain Wattle - Did you ever hear of Captain Wattle?
Change for a Guinea - Jack Binnacle met with an old shipmate
Cheap Experience - I were but in our village a country clown
Clemency - Say, soldier, which of glory's charms
Echo - When from the glowing blush of morn
Every Man's Friend - Come, all jolly topers! the toast as ye pass
Father, and Mother, and Suke - Says my father, says he, one day, to I
Gallant Tom - It blew great guns, when gallant Tom
Grizzle - 'Twas one morning in May, the weather but queer
Jack at Greenwich - We tars are all for fun and glee
Jack Junk - 'Twas one day at Wapping, his dangers o'erhauling
Jack's Advice to His Friend - Why, Tom, thou'rt a seaman; and may ev'ry wind
Jack's Alive - Sweet Nancy Nouse and Jack Jibboom
Jack's Claim to Poll - Would'st know, my lad, why ev'ry tar
Jack's Fidelity - If ever a sailor was fond of good sport
Jacky and the Cow - There were Farmer Thrasher, and he had a cow
Kickaraboo - Poor Negro say one ting,—you no take offence
Life like a Troubled Sea - This life is like a troubled sea
Life's Weather-Gauge - I'm for Tom Tiller's golden maxim
Love at Fifty - When I told you your cheeks wore the blush of the rose
Lovely Nan - Sweet is the ship, that, under sail
Love's Probation - 'Tis said, that love, the more 'tis tried
Mad Peg - The gloomy night stalk'd slow away
Magnanimity - When once the din of war's begun
Meg of Wapping - 'Twas Landlady Meg that made such rare flip
Moorings - 'I've heard,' cried out one, 'that you tars tack and tack'
Mounseer Nongtongpaw - John Bull, for pastime, took a prance
Mrs. Runnington's Wig - Mistress Runnington wore a wig
Nancy - You ask how it comes that I sing about Nancy
Nancy Dear - Why should the sailor take a wife
Nancy's the Name - One Shakspeare, a bard and a poet of fame
Nature and Nancy - Let swabs, with their vows, their palaver, and lies
Ned That Died at Sea - Give ear to me, both high and low
No Good without an Exception - The world's a good thing; ah! how sweet and delicious
One - Up the Mediterranean
Philanthropy - Tell me not of men's follies, their whims and caprices
Poll and My Partner Joe - I was, d'ye see, a waterman
Pope Joan - The board is dress'd, come deal away
Rational Vanity - Man, poor fork'd animal, why art thou vain?
Second Thoughts Are Best - 'I never shall survive it,' cried Lumkin in despair
Smiles and Tears - The weather, the land, and all those that dwell in it
Tack and Half-Tack - The Yarmouth Roads are right a-head
The Advantages of Toping - Some say topers should never get mellow
The Anchorsmiths - Like Etna's dread volcano, see the ample forge
The Barber's Shop - 'Twas Saturday night; six went the clock
The Best Bower Anchor - I have oftentimes thought it a wondersome thing
The Can of Grog - While up the shrouds the sailor goes
The Flowing Bowl - Of all Heav'n gave to comfort man
The Irish Wake - Life's as like as can be to an Irish Wake
The Irish Wedding - Sure won't you hear what roaring cheer
The Labourer's Welcome Home - The ploughman whistles o'er the furrow
The Lady's Diary - Lectur'd by Pa and Ma o'er night
The Last Shilling - As pensive one night in my garret I sat
The Look-Out - Old Cunwell, the pilot, for many a year
The Lover - Long by some fair one was I trick'd
The Nancy - Mayhap you have heard that as dear as their lives
The Nautical Anatomist - Jack Jigger, a curious and whimsical tar
The Perpetual Motion - Lord help you poor lubbers ashore
The Sailor's Defence - If tars of their money are lavish
The Sailor's Journal - 'Twas post meridian half-past four
The Sailor's Lesson - Since, Jack, thou'rt a seaman's son
The Sailor's Maxim - Of us tars 'tis reported, again and again
The Sailor's Will - The network stow'd with hammocks all
The Sapling - In either eye a ling'ring tear
The Sheepshearers - Our sheepshearing over, surround the gay board
The Shipwreck'd Tar - Escap'd with life in tatters
The Soldier's Farewell and Return - Though hard the valiant soldier's life
The Soldier's Funeral - The martial pomp, the mournful train
The Spectre - Cosmelia the fair, of the virtues the care
The Tear of Sensibility - When to man the distinguishing form
The Thrasher; or, A Jug of Brown Ale - Can any king be half so great
The Token - The breeze was fresh, the ship in stays
The Veteran in Retirement - Though laid up in port, and not outward bound
The Veterans - Dick Dock, a tar at Greenwich moor'd
The War is Over - Come, come, my lads! the war is o'er
The Welcome - What if the Sailor boldly goes
The Wig Gallery - Walk in, walk in! each beau and belle
The Wind and the Rain - All nature was sportive, serene was the morning
Three Cheers - When to weigh the boatswain's calling
Tol de Rol - I went to sea all so fearlessly
Tom Tackle - Tom Tackle was noble, was true to his word
Tom Tough; or, Yo Heave Ho! - My name, d'ye see,'s Tom Tough; I've zeed a little service
Tom Truelove's Knell - Tom Truelove woo'd the sweetest fair
True Courage - Why, what's that to you if my eyes I'm a wiping
Tue Cornish Miners - Why, measter, damn tha! whoa beest thee?
Variety in One - In one shouldst find variety
Water-Cresses - Jack come home, his pockets lin'd
Who Cares? - If lubberly landsmen, to gratitude strangers