Here's a (hopefully) complete list of all of the souvenir items that I accumulated during my trip. The ones that came free of charge are marked with a *.

Bags*
Grandma was smart. Every time someone asked if we wanted a bag, she said "yes". She even specifically asked for a bag sometimes. They make great souvenirs and they're cheap.

Harrod's (large)
Harrod's (small)
Hamley's
British Museum (x2)
Transport Museum
Historic Scotland (museum)
Davenport's Magic Shop
Tower of London
Hard Rock Café

Fliers*/magazines*/newspapers*
"This is London" travel guide
Kensington Palace (we didn't go there)
"Connoiseurs Scotland"
"Where"
The London Paper
Welcome to Edinburgh (x2)
Hatchard's: a short history
Camera Obscura
The Real Mary King's Close
Pollock's Toy Museum
Edinburgh Castle
Daily Telegraph
Celsea Physic Garden

I also got 5 maps (free)

Tickets
Tower Bridge Exhibition
City Sightseeing London
The Original Tour
The London Eye
We Will Rock You
London Underground Day passes
Edinburgh Castle

General
Tower Bridge Photgraphs and Magnet
Madame Tussaud's Wax Museum Souvenir Keychain Featuring Johnny Depp and You
Rapid-Fire wooden rubber band gun with target and 10 rubber bands
Hard Rock Classic Tee
Headphones from the Original Tour*
Jumping frog (balloon legs, when you pump air into said legs they expand, thus allowing the frog to spring into the air)
Air Canada Comfort Kits*
Napkin from Harrod's*
Diet Coke Bottle from the Club Lounge*
Jars of Ketchup and Maple Syrup
Magic Wallet
Working Replica Catapult wih pencil sharpener
Sugar/sweetener packets with Harrod's Logo*
"Wheel" keychain from Royal Yacht Brittania
Brittania Bear Keychain from " " (for Michelle)
Replica Roman Coins from British Museum (for Michelle)
Bagpiping Bears (from Grandma, one for each kid)
Egyptian Golden Cat earrings from British Museum (for Katherine)
Harrod's Biscuits (Chocolate Macademia nut/Ginger, for Mom, Katherine, and Michelle)
Hand-cranked music box ("whistle while you work")
Underground Logo Keychain from Transport Museum
Rosetta Stone-shaped keychain from British Museum
Hard Rock Café Pin*
Hard Rock Café rotating guitar keychain
"bagpipes" keychain
"Wow" (super-awesome magic trick)
"Count of Monte Cristo" escape (binds hands, feet, and neck)
Bedlam Cube
Eastsheen double, triple, and quadruple 2x2x2 Rubik's apparatuses (picture the 2x2x2 Rubik's cube but linked at the corners of other 2x2x2s)
Giant Inflatable HoverDisk (seems to have a mind of it's own)

If i've forgotten anything, i'll be sure to post it