Unfortunately, it's difficult to predict what your birth will be like.
If not for the need to stay an extra night, mine would've been well under 6K (including consultant's fee). This was in Portland.
I had a natural (no meds, not even gas & air) labour until I got to the second stage and DS got stuck as was coming sideways. So I had to have an epidural (at 2nd stage 
:() and a ventouse delivery. Had I not lost so much blood, they would've let me go home straight after. But because I had to stay a second night (after a 23 hour labour & birth ), the total cost was almost 10K (nursery fees alone were about 1200, though we never used it).
The total cost depends on whether you've had a consultant follow your pregnancy throughout as well. Most have a fixed fee for pregnancy + delivery.
Why not call a few hospitals and ask what their fees are, normally? They have no reason to withhold this information and I believe they're actually obligated to tell you.
Just remember that you might end up needing things like an epidural (even if you don't plan on it), assisted delivery or even a C-section. That's aside from the normal - room fees, consultant fees, nursery fees, paediatrician fees (if you're having your baby checked after birth - good idea, btw). And do ask what they charge for a second night's stay (should you need one) - this is less than the inial 24hr charge, but still considerable.