Two different ratings boards, two different ratings. The BBFC rated "Skyrim" 15. PEGI rated "Skyrim" 18. The original UK release of Skyrim used the BBFC rating, but the Legendary Edition uses the PEGI rating.
There's nothing "extreme" in the expansions that pushes the age-rating up; the original 'vanilla' version of "Skyrim" was also rated PEGI 18 for (quote) "Extreme violence - Violence towards defenceless people."
It was a similar story with "XCOM: Enemy Unknown" (2012) - the BBFC rated that game 12, but PEGI rated it 18. Two different ratings boards, two different ratings.