In reply to Blunderbuss:
Very; and early. Not hugely helpful I'm afraid, but a precise time is probably anyone's guess. I'd personally aim to be there well before 9am (and it's a 3-hour drive for me). It soon gets parked up, and some of the congestion and numpty parking is horrendous.
A sensible alternative would be to drive to Keswick and get the bus down Borrowdale from there. That way you're not becoming part of the problem. It does tie you to the timetable though