The sphinxes are recent castings and Cleopatra's Needle doesn't really have anything to do with the Egyptian Queen of the same name, however it is a genuine Egyptian obelisk dating from the reign of Thutmoses III around 1450BC. It was one of a pair found in Heliopolis and given to the British as a gift in 1819 by the Egyptian ruler Mohammed Ali, but they refused to pay for it to be transported until 1877. The pontoon it was on capsized during a storm off France and six people died, but it remained floating and it was eventually towed to London. The other obelisk of the pair is in Central Park in New York city.
The damage you can see on this sphinx's pedestal was caused by a bomb during the first world war. This happened on September 4 1917, during the first raid made by German planes against London. There's similar damage from world war two preserved on the walls of the Victoria and Albert museum.
