Well.. GoinSideway.. it's true that by not doing IELTS you are saving some money. But isn't it worth the insurance that the uni can't reject you because of your IELTS? It will be a real pity if you were "expected" to have IELTS results ready for verification and you've failed to do that.
I suggest that "to be on the safe side" you should take it. It may be expensive, but if it costs you, your place at Imperial... that will be a real pain in the ***.
PS. My head of 6th form is also a bit weird... Is it just us, or is it a thing with head of 6th form...??