I suggest that 1981 was the absolute nadir of utility cycling in Britain. As evidence for that I present, courtesy of Graham Smith, this diagram from the December 5, 1981 issue of the The Economist.
This also gets it wrong by putting "Car" where it should have "Bus", but that's another story.
Note: Liz Batty has pointed me at the MINITRAM planning society.
For a real-life example of modal share at different distances, if cycling is actually enabled, here's a chart of data from Amsterdam in 2012 (source "Traffic Planning in Amsterdam", via Drawing Rings). There have been some major active travel improvements since 2012, most obviously around the railway station, so the modal share of cycling is likely even higher now.
Cycling is the majority choice from 1 to 5km (3 miles), and the plurality choice up to 7.5km (5 miles).