The plot to the left shows the distribution of heights of American women, ages 20 to 29, according to the 2007/2008 census. Data here. I couldn’t find data on UK heights, but it should be similar. Data for the heights of men are similar but shifted up a bit. The circles are the data and the line is fit of a Gaussian function to this data. The most probable heights are around 165 to 170 cm (5 ft 4 in to 5 ft 6 in). The width (standard deviation) of the Gaussian fit is 7 cm.