There is availability at rates far less than you are stating, at least for the random date I chose. For instance at the Marble Arch Marriott



Perhaps it's the dates your looking at, the properties you'd like best or maybe you are putting 3 adults in the search instead of 2 adults and 1 child. Or it's a combination of the previous 3.

Ethics aside, I think if your kid is a child you're probably ok but if your kid is an adult, not so much.