Fawley is a village and civil parish in Hampshire, England. It is situated in the New Forest on the western shore of the Solent, approximately 7 miles south of Southampton. Fawley is also the site of Fawley Refinery, operated by ExxonMobil, which is the largest facility of its kind in the United Kingdom. The decommissioned Fawley Power Station is also …Fawley is a village and civil parish in Hampshire, England. It is situated in the New Forest on the western shore of the Solent, approximately 7 miles south of Southampton. Fawley is also the site of Fawley Refinery, operated by ExxonMobil, which is the largest facility of its kind in the United Kingdom. The decommissioned Fawley Power Station is also located less than a mile to the south east of the village.