Please note I am not affiliated with any of these companies. I have bought things from them but I make no special guarantees for them:
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Maplins http://www.maplin.co.uk/
There is a shop in Tottenham Court Road where you can just walk in or reserver stuff and pick it up the same day. You can also order online. They are useful for batteries, power supplies, basic kits and large items that you need to see before buying. They are pretty bad for small electronic components though. Don’t expect much reliable knowledge from the staff …
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http://www.quasarelectronics.com/
Mail Order only. They sell super useful kits that do basic interaction.
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http://www.robot-electronics.co.uk/
Mail Order only. These guys sell some great sensor components as well as motor stuff.
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http://www.coolcomponents.co.uk/catalog/
Mail Order only. Lots of useful stuff including Arduino boards
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Mail Order only. Cheap and quite quick for variety of electronics stuff