According to Official Guinness Records,
The greatest position change for a Premier League football (soccer) team in consecutive seasons is 13, achieved by Leicester City F.C. (UK) from 24 May 2015 to 2 May 2016.Leicester City F.C. finished 14th at the end of the 2014/15 Premier League season with a total of 41 points. In the 2015/16 campaign they finished 1st and were crowded the Premier League champions with two games to spare.
For a complete list of 2016 records, please visit 2016 Guinness Records in United Kingdom.