How should black play against this system?

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mnag

Agreed, but you may want to find out what good players do with the pawns on c7, d6, e5 and f5. Sometimes in KID vs London White can place pieces on d5, for instance, a knight or after White plays dxe5, he can also place a queen on d5.

MyCowsCanFly

The motiffs differ somewhat depending on if it's the Tarzan variation of the London or the Barry. The Tarzan has Qd2 to support the dark square bishop exchange.