According to the US/UK Tax Treaty, as written, UK State Pension payments received by US citizens residing in the UK are taxable in both countries.
The Technical Explanation of the US/UK Tax Treaty gives rise to the question of whether the wording in the Treaty reflects the intentions of the authors of the Treaty, and in fact, if the intention was for it not to be taxed in the US in these circumstances.
Some advisors believe it should be declared on a 1040 return as per the Treaty, others believe it shouldn't. In other words, situation normal for the reporting requirements for USC expats. (Possibly issue #1,876 out of the 14,734 questionable issues concerning expats, or perhaps not.) I'm not sure the IRS really cares.
For a USC resident in the UK and receiving a UK State Pension payment who is in the 40% UK tax bracket, it may be wise to declare it on a 1040. If a stance is taken not to report it, the TP loses all tax paid to the UK on the pension (Form 1116) similar to US SS. If it is declared, the tax paid to HMRC can be claimed. For 1116, the IRS will care.
In any case, blanket statements on this issue should always carry a caveat, one way or the other.