Your barrels, at least, of your Manton were made in Belgium. The third image clearly shows ELG over star, the mark of the Liége Proof House - ELG = Épreuve Liége. The intertwined and cursive EL also shows the same source. Such barrels were exported in the rough state, proofed but neither struck nor blacked, to many Birmingham and London gunsmiths at the time. You can be 99.999999% certain that Manton, makers of some of the very finest guns, smooth and rifled, of the period that ended with his bankruptcy in 1826 and his death in 1835, had little or nothing to do with your percussion shotgun, apart from the gratuitous use of his surname.
Joseph Manton's weapons remain some of the most highly sought-after designs of the flintlock age and can fetch more at auction than Holland & Holland's shotguns. His workforce included James Purdey (who went on to found Purdey's), Thomas Boss, William greener, Charles Lancaster and William Moore. These five skilled craftsmen established major gun firms, most of which are still in [a very lucrative] business.
Many Belgian-made guns like this were sold using famous names - often slightly misspelled to 'avoid confusion'. My 1906 Sears catalogue has many pages of such arms. I have no doubts that your is one such arm, as Mr Manton is not known for his percussion ignition guns of any kind. He DID however, pioneer another form of ignition - the tube (or pill) lock, which was an improvement over Alexander Forsyth's so-called scent-bottle lock. Rather than storing a reserve of fulminate in a container, it utilised a single-use pellet or pill. The hammer of the gun was sharpened; when it fell, it crushed the tube/pellet, causing the fulminates to detonate.
Although more reliable than Forsyth's design and adopted by many sportsmen during the Regency period (and a variant for the Austrian army), it was quickly overshadowed by the percussion cap, which was adopted by the armies of Britain, France, Russia, and America to replace the flintlock.