Ivy growing on brick walls has several advantages. It keeps wall temperatures cooler and can possibly lower cooling costs during the summer if the brick wall is on your home. However, the ivy can stain and damage the bricks and mortar over time. It is also extremely difficult to remove. Sometimes, removing ivy not only reveals possible damage, but can also cause damage during the removal process.
Cut off a small section of ivy--about 3 feet by 3 feet--in an inconspicuous spot to check how much the ivy is rooted into the brick. See also what the bricks look like underneath. The bricks may be stained or damaged and in need of repair. Wear garden gloves for this.
Cut the remaining ivy close to the wall with a pair of hand clippers. Start near the top and work your way down. Do not pull. Pulling off ivy is more likely to cause damage.
Wait until the suckers left behind dry up and turn a dark color. This could take a week, but don't wait longer than two or three weeks when the suckers will be too difficult to remove and might oxidize and stain the bricks.
Scrub the dry and dark suckers with a stiff fiber brush dipped in water mixed with laundry detergent. Use about 1 tbsp. of detergent per gallon of water. Again, start at the top and work your way down.