In the Civil War period Buckshaw Hall (Higher Buckshaw) was in the occupation of Edward Robinson, one of the Justices of Lancashire. In 1644 he was described as a Major in the Parliamentarian army. It was he who appointed the Registrar of Leyland in 1655 and 1656. He appears to have made his peace with the authorities after the Restoration, and died 7th January 1680/1.
That might give a clue about when the Wilcock family took occupation of Buckshaw.
There are few early mentions of the Wilcock name in Leyland parish, which includes Buckshaw. The earliest is Richard Wilcocke, buried at Leyland in October 1653 (no township mentioned), Robert and John Wilcock (both of Leyland) in November 1667. The next Wilcock is Christma Eve 1702 when John son of John of Houghton was baptised. The conclusion must be that they arrived from elsewhere (they had real money if they bought Buckshaw, so could travel) or that they were Roman Catholics. My guess is the latter, since they avoided putting the surname in later Leyland registers too.