I went through this procedure but opposite countries, I still currently live in US. I'm a DC and wanted to get my son his UK citizenship after we got his US passport (he was born in US). I remember I just filled out paperwork enclosed my UK passport, UK birth cert and I think my marriage certificate plus $$ and he got his UK passport without any problem. As Mother he can automatically qualify for it. With my daughter it was a different process as she was adopted from China, so we had register as a UK Citizen and then get her UK passport. Although my son has citizenship through me and a UK passport he has no other documentation, which means that if something were to happen he has more of a paper trail than my daughter to prove his citizenship. I'm not even sure if we can pursue my son's UK registration after the fact, it's something I have to look into once we are over.
I've read various oppionions on different sites about just having a passport to prove citizehship. With the rules and regulations changing in immigration it maybe wise to also register him as a citizen as well. We could not get our daughters US passport untill we had registerd her as a US citizen, even though she had been reissued with a US birth certificate after the adoption. You may not have an option but to go through the registration process, before you get the passport. It's wise to check it out now with time before you travel.
On a footnote to this, my ex husband was born in the UK but had US citizenship through his Dad. My ex had US passport but no registered citizenship. When he was sponsoring me back in 1990, he was questioned by INS about his status because he had no other proof except US passport. They told him he should have had a record of naturalization. However, the matter was not pursued any further than a conversation. I'm not sure if this would be so easy now post 911
I hope this helps
