The general savings clause in Article 1(4) of the UK/US double tax treaty, which allows the US to tax its citizens without regard to the majority of the treaty, is subject to the exceptions contained in Article 1(5). Article 1(5) provides that these exceptions include Article 17(5). Accordingly, Article 17(5) applies to US citizens.
Article 17(5) deals with maintenance payments (in UK terminology) or alimony (in US terminology). It provides that alimony paid by a resident of the UK to a resident of the US is exempt from tax in both the UK and the US. This is subject to the exception that were the payments tax deductible in the UK, they would be taxable only in the US.
Since alimony is not tax deductible in the UK, the exception does not apply. (The exception is in the treaty in case the UK amended its tax rules to allow for the deductibility of alimony; this had applied until 1988).
Accordingly, the alimony paid by a US citizen UK resident to a US citizen is exempt from tax in the UK (and so, the UK will not apply withholding taxes) and in the US.