You won't be alone, there is a rack of seating at the back of the departure hall and I would guess three quarters of the people there are waiting for the witching hour.

You can check luggage for a fee into the left luggage facility on the Arrivals level, next to Marks and Spencer. Or enquire about any Airport Upgrade Promotions for sale (and if the answer is no, or it's too expensive, the agent may take pity on you and may press the override button).