Brick is not used in England because of cost or strength. Brick is used because historically London has burned down completely leaving many people homeless. Brick ensures that a fire will not spread from one hour to another. When you build a densely packed city it makes perfect sense to use fireproof material at any cost. When your houses are spread farther apart you rely your neighbor's house fire not taking your house down so flammable building materials is much less risk.

In fact brick is NOT always as strong as wood! Brick is stronger under compression, and it feels harder, but under tension brick is much weaker than wood.