Traveling from US to Dublin via Birmingham (UK). How much time do I need for a layover? [closed]

I have a flight booked from the US to Birmingham which gets in at 7:10am. I am planning to book a separate flight from Birmingham to Dublin which leaves as soon as possible after I arrive--no need to leave to the airport or anything.

Will I have to go through customs in Birmingham? What is the earliest I should look for in a flight from Birmingham? They have flights around an hour after my arrival, which seems a little tight; impossible if i have to go through customs. The next flights are around noon and cost about twice, but it seems like that might be my only reasonable option.