There are several 'stations' in your tour around the museum where you get a little card that you can have handstamped with a special postage ink stamp.
They have a nice display of old post boxes. Did you know that they change the post boxes every time there is a new king or queen?
The museum also has a display about how the mail was transported around the city and country.
Do make time to visit this museum next time you are in London. It's not a huge museum so it doesn't take all day to go through. Since it's near St. Paul's Cathedral, once you get done the harrowing climb there, be sure to visit the National Postal Museum.