Great Western Coffee Shop

Total station entries and exits, 2016/17 2,939,350,914 - source - ORR station figures for 2016/17
So that's 1,469,675,457 journeys (each comprising an extra and an exit)

There were 223,287,904 interchanges - so that's one interchange per 6.58 journeys, or 15.2% of journeys involving a change of train.

Words of caution
* Some journeys involve multiple changes which makes that 15.2% figure a bit high
* These are National Rail interchanges, so changes to the Underground, etc, aren't included making the 15.3% a bit low.
* These figures do not take into account changes to other public transport - predominantly buses.

Theory  ;) - it is important for the rail industry to consider connectional times as well as how long the trains actually take to make individual journeys when looking at people's total journey time in the light of comparisons to other modes and to practicality of journey on a daily basis.

Corollary If each change takes 5 minutes, then total wait time between trains for rail passengers is 18 million hours per annum.   People's time is priced (in economic value) between £5 and £30 per hour (WebTag, 2014 figures) - taking an average of £10 per hour that means that each minute extra in connection time costs the economy £3,000,000 annually.   


(http://www.wellho.net/pix/webtag14.jpg)