There is no outbound Immigration control in the UK so the only people to whom you would show your passport on departure would be airline staff at check-in and at the gate. They will record your details for US Immigration so you should show them whatever passport you intend to use to enter the USA. They won't know what passport you used to enter the UK so that doesn't come into the equation.

Needless to say you want to use an EU passport to enter the UK.