Actually the Man museum has storage lockers. Check the size of your luggage to make sure it fits. It looks like the typ. school lockers type. They need it since no purses are allowed for the tower visit so they provide lockers for visitors.
Most of the museums have very limited storage space (no bigger than a backpack). I did not see luggage storage when I was there last. The room is not big to begin with, and with the number of visitors, I'd be surprised if they would want the responsibility.
Not sure but may be clock room is available
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