It's a 681. The 681 has fixed sights built into the topstrap like the one shown. A 686 has raised adjustable sights that would be clearly visible.
Unknown revolver
A snub-nosed revolver is used by Tyrone and Vinnie throughout the film. The weapon is most noticeably seen in the hands of Vinnie when he and Sol attempt to rob the bookies.
when Vinny (Robbie Gee) threatens Bullet Tooth Tony ( Vinnie Jones) he carries a Heckler & Koch P7M8 with black finish. It is implied that the gun, along with Sol's Heckler & Koch P9S are blank-firing 'replicas'.
Heckler & Koch P9S
Sol(Lennie James) uses a Heckler & Koch P9S to threaten Bullet Tooth Tony. The gun is also implied to be a 'replica', but they should not be able to fire blanks (like they do in the movie).
IMI Desert Eagle Mark VII
Bullet Tooth Tony (Vinnie Jones) famously carries a "Desert Eagle .50" (however, a close inspection of the bore reveals his gun is actually the .357 Magnum version). Cousin Avi (Dennis Farina) also tries to use the Desert Eagle in a later scene.
Unknown compact pistol
In a flashback sequence, a man is shown shooting Tony six times with a pistol, hence giving him the name "Bullet Tooth Tony".
Unknown compact pump action shotgun
It is seen briefly in the introduction, Boris the Blade pulls it out of his safe and cocks it.
It is also seen on a table when Boris sells Franky Four Fingers his revolver, and later it is seen again in Boris' safe when Cousin Avi, and Bullet Tooth Tony raid his home. A similar shotgun also appears to be used by one of Mickey's friends, Darren, (Jason Flemyng) to shoot one of Brick Top's henchmen at the campsite.
It's either a Mossberg 500 Cruiser or a Reminton 870 fitted with a pistol grip. I've seen the film and the gun has a pistol grip.
Franchi SPAS-12
Vincent (Robbie Gee) buys a compact version of the SPAS 12 for the heist of Brick Top's (Alan Ford) bookie. Sol fires the shotgun twice, first to blast a hole in the wall and then into the roof
Unknown pump action shotgun
Various pump action shotguns are carried by Brick Top's thugs and the Pikeys, who use their weapons to ambush and wipe out Brick Top's men at the campsite.
Boris 'The Blade' Yurinov fetches an AK-74M with a GP-30 grenade launcher and magazines taped 'jungle-style' from his home after escaping capture and being hit by a car.
Boris 'The Blade's' gun collection
Boris 'The Blade' Yurinov has a collection of weapons which is shown three times during the movie: first when he is selling the S&W 681 to Tommy, when he returns a revolver to Franky Four Fingers and later when Cousin Avi and Bullet Tooth Tony break into his secret cache to look for the diamond. Feel free to ID what weapons are in there.