There's a seperate queue at the airport for holders of EU passports. You just enter the UK on your Spanish passport, and put your US one away. All the UK is interested in is if you are an EU or UK national, as EU nationals don't need visas.
There are many, many people with US/other national citizenship and it's not a problem at all.
When you leave and enter the US, just do so on your US passport.
If you are questioned in the US, just tell them you are a dual national. That's not against the law.