ACM Park, in charge of 11 group, only had 16 squadrons to fight that battle.
He was expected to provide continuous air cover for the beachhead, and thus there was a conflict between providing continuity of cover and strength.
He choose to increase the size of the patrols at the expense of their frequency.
It was the stronger but less frequent cover that gave rise to the impression that the RAF was absent from the battle because there were occasions when the Luftwaffe took advantage of the gaps between the patrols.
To enable the evacuation to proceed without interuption as far as was possible, the fighters object was to prevent the Luftwaffe reaching the beaches.
Thus, as Tocsin has pointed out, most combats took place at high level and away from the beach area.
A few stats will show what the the RAF achieved.
In the 9 days of the battle Coastal Command flew 171 sorties, Bomber Command 651, and Fighter Command 2,739.
Fighter Command lost 99 aircraft against the Luftwaffe's 132.