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Read the series of articles about The London and North Western Railway from One Hundred Years of British Railways in The Engineer here:
The London and North Western Railway (LNWR) was a railway company that existed between 1846 and 1922 and is an ancestor of today's West Coast Main Line. It was created by the merger of three railway companies: -
1846 The London and North Western Railway was incorporated under its present title.
1875 See 1875 Number of Locomotives where they are listed first with 2,019 locomotives
1888 See Locomotive Stock June 1888 where they are listed first with 2,323 locomotives.
1908 The line is 1,719 miles in length, while 114 miles are partly owned. 
1923 Total route mileage was 2,667.5 miles
1923 The LNWR became a constituent of the London, Midland and Scottish Railway (LMS) when the railways of Great Britain were merged in the grouping of 1923.