OK, slight edit there. At some UK airports, you just walk out the door, unless you needed to use the Red customs phone to call someone over, or they knew you needed to use the Red customs phone and caught you leaving without doing so. (eg you're a minor celeb and posted a load of photos on twitter of a NY shopping spree, then tried to exit in Manchester without using the magic Red phone to let them know you needed to pay taxes...)
At most UK airports, there's just a shared baggage hall for Domestic + International flights. There, after your UK connection, you exit through the most strict door for you + your bags. (If you cleared EU customs with your hand luggage in Dublin, but your bags were checked through to LCY, use Green not Blue as not all of your stuff is EU cleared by that point. Well, Green or Red / Red phone)