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The Lewes and Uckfield Railway Company was incorporated and secured on 27 July 1856 by the passing of an Act to construct a line covering the 7.5 miles to Uckfield from a point 1.5 miles (2.4 km) north of Lewes, to be known as Uckfield Junction, on the London, Brighton and South Coast Railway Brighton to Hastings line.
The LBSCR supported the company's proposals, and a connection linking Lewes to Uckfield was opened on 11 October 1858 to goods, with passengers one week later. The line, much of it through low-lying meadows, required only three minor cuttings and a number of bridges, including one over the Ouse Navigation.
The LBSCR absorbed the Lewes and Uckfield Railway Company in 1864.
The above information is taken from the Wikipedia entry for the Wealden Line.