Skivington joined London Wasps in 2003, In 2008 he signed a contract keeping him at the club until 2010.
On 14 April 2010, it was announced that he would be moving away from Wycombe to join Premiership rivals Leicester Tigers at the end of the season. His final game for Leicester was the Premiership final at Twickenham against Harlequins.
On 23 January 2012, it was announced that he would be joining London Irish from the start of the 2012/2013 season.
On 28 January 2010 he was named captain of the England Saxons side to play Ireland A at Bath's Recreation Ground on Sunday 31 January. He led his team to a 17–13 victory, and again against Italy A.
Phil Dowson's call-up to the full England squad saw Skivington also lead the Saxons throughout their victorious Churchill Cup campaign in summer 2010.