Could you not travel on your US passport? If you've sent it away, you can get another passport at the embassy if you can prove that you have travel booked. Bit of a pain, but I've done it.
I've also entered the UK on my US passport only during the period while I was waiting for my UK passport. If you've had the ceremony, they have to let you in because you are a UK citizen. In my experience, the border guards are happy to let you in, especially if you act proud and happy to be a UK citizen.
You can also contact your MP for help speeding things up, especially if your travel is extremely important. I flat out told my MP the truth that I was only trying to go back to the US for a kite festival and it certainly was NOT a life or death situation, but mysteriously my finished passport arrived just when I needed it anyway and maybe she helped it along.