The branch in question was a connection to Astley Green Colliery, on the northern bank of the Bridgewater Canal between Astley Green and Higher Green. The colliery was sunk in 1908 by a subsidiary of the Clifton & Kearsley Coal Company, and was the southernmost on the Lancashire Coalfield.
The pit head was alongside a horse-drawn tramway which connected Yew Tree Colliery in Tyldesley with a wharf on the Bridgewater Canal at Astley Green. According to Wikipedia (
https://en.wikipedia.org/wiki/Astley_Green_Colliery) this was built "by about 1851" but it appears on an Ordnance Survey map published in 1849 and surveyed 1845-6, so it must have been sometime in the mid-to-late 1840s. Subsequently this tramway was connected at Tyldesley to the Eccles, Tyldesley and Wigan L&NWR route and to the labyrinthine Bridgewater Collieries railway system across Linnyshaw Moss. The tramway had fallen into disuse by 1913, and the southern end was bought by the Clifton & Kearsley Coal Company for use at Astley Green Colliery. The route northwards to Tyldesley was dismantled.
The branch northwards from the Liverpool & Manchester had junctions facing both east and west, and was built concomitantly with the sinking of the colliery. Similar methods of construction across Astley Moss were employed as those used by Stephenson to cross Chat Moss, with brushwood overlain with pit waste providing a foundation for the rails. The bog beneath the rails was up to 28 feet deep in places. Production began at the colliery in 1912, with the railway connection to the L&M complete by the opening of the colliery.
A new railway connection was later opened to the Bridgewater Collieries lines at Boothsbank tip, around 3/4 of a mile to the east. This linked Astley Green Colliery with the rest of the Bridgewater Collieries railway network, along with their workshops and and larger tipler at Boothsbank, and allowed the closure of the small tipler that had been built at the end of the original horse-drawn tramway. According to one source this eastwards link was built in 1930, but it does not appear on OS maps until 1949; there is no evidence of this link on the 1938 survey.
For many years one of the main customers for Astley Green coal was BR. With the disappearance of steam in 1968 the pit was one of a number in the Lancashire area that came under scrutiny, and the last coal was wound on 3rd April 1970. It is now the Astley Green Colliery Museum.
Incidentally there was also, for a time, a branch off the L&M northwards just a short distance to the west. This left the main line more-or-less at the point where Flow Moss Cottage station had been, and served Britannia Moss Litter Works just to the north of the railway. The 1891 OS map shows two tramways continuing onto Bedford Moss. In 1896 the British Moss Litter Company had been founded originally by amalgamation of smaller companies who extracted peat around Crowle and Thorne in Yorkshire; by 1905 they had taken over the Britannia Moss Litter Works and considerably extended the workings and the tramway system used to transport the peat. The demand for Litter Moss dropped off after the First World War, and the peat works closed sometime before 1929 (I can't pin it down any further than that though.)