Air pig - 'Other factors in this debate are missing, ACM Dowding as AOCinC of Fighter Command had numerous things to his advantage, by his foresight he developed an air defence system that exists to this day, was in receipt of ULTRA information, a privilege accorded to few very senior commanders...'
Did the Enigma decodes have an input in the Battle of Britain?
Hinsley et al in 'British Intelligence in the Second World War' suggests that although British intelligence (all of it) was improving this was not a major factor in the Battle of Britain. It seems up to then mostly strategic intelligence was being derived. Hinsley credits 'the tenacity of British resistance' to the GAF's failure.
Also as Hinsley points out, this was the first major defeat Germany had suffered and as such represents a turning point in the war.
I agree it is difficult to know what would have happened had we lost the BoB but it surely would have affected the will to continue. Air superiority is not everything as the Normandy landings showed but it's a big help.