The 11 ft 2" figure definitely predates the Big Four Era - The Board of Trade Requirements for 1902 mandated that for all new railways "The intervals between adjacent rails, where there are two lines only, or between lines of rails and sidings, not to be less than 6 feet. Where additional running lines are alongside the main lines, an interval, of not less than 9 feet 6 inches to be provided, if possible, between those additional Lines and the main line. This is what gives rise to the 11 ft 2" centre to centre dimension.
See - http://www.railwaysarchive.co.uk/documents/BoT_Requirements1902.pdf
However, the above is an annotated copy of the 1892 edition which stated that the distance "should not be less than 6 feet". Presumably it was felt in the late 19th century that the use of the word 'should' was perhaps a reason why some companies were perhaps not necessarily following what had been established as a standard in the Victorian Era.
Therefore whilst some earlier railways may have built to a closer interval originally, it is likely that the spacing would have increased to meet the Board of Trade Requirements during subsequent renewals.