You don't tell us what make of mower, nor the engine type, but the following socket will probably help you as it fits both 10mm and 14mm hex plugs. Not expensive at £6.99 either.
http://www.halfords.com/webapp/wcs/stores/servlet/product_storeId_10001_catalogId_10151_productId_567025_langId_-1_categoryId_255216
ChicksFan, August 2013