Here is the new baggage policy. Apparently bags far bigger than yours can go in the lockers:

Hand baggage allowances… changing from 5 July 2006
The hand baggage policy will be the first to change from 5 July 2006.
All passengers will be able to carry one standard-sized bag and one briefcase, laptop computer bag or equivalent on all flights.
The maximum size of the bag, 56cm x 45cm x 25cm (22in x 18in x 10in) has been set in line with the UK Department for Transport recommendations. Passengers must be able to lift their bag unaided into the aircraft overhead locker.
The briefcase, laptop computer bag or equivalent must fit under the seat in front

Anyway, on the upper deck, the crew can store it in the coat area in the galley where you can get it to when you want. Another advantage of being upstairs and in a window seat is that you get a lot of storage space in the locker next to your seat for anything you may need during the flight.