In reply to midgen:
Wasn't Easter Sunday raining though? I went Saturday afternoon in lovely weather and it was super busy. Spaces in the plantation carpark though when we got there mid afternoon, but lots of pretty silly parking half on verges half on the road which was partially blocking the road.
OP - get a guidebook and look for places you've not heard of before. Chances are they will be quieter, if not you would have heard of them. Parking can be busy everywhere as lots of people beyond climbers visit the Peak, but maybe try looking at the venues west and north of Darley Dale.