The latest immigration directorate instructions (dated July 2011) don't say a court order is necessary in every case, but the UKBA has a duty to protect a child's welfare under law. It looks like UKBA in NY is taking a tougher stance, either in this particular case or in general. Because of the length of time your application has taken, it seems probable that your application was referred to the caseworking section in London and their decision reflects the conclusion reached by the UK unit. It may be that absence of father's particular on a birth certificate and a notorised letter is not enough and a more objective evidence is required. They do state that a custody/residence order by a US court can be taken as conclusive evidence of sole responsibility.
http://www.ukba.homeoffice.gov.uk/s...Is/idischapter8/section5a/annex-m?view=Binary