Seems to me (going by what the treaty and technical explanation seem to me to say) that the UK would probably agree that yours is a US Government pension and therefore exempt from UK tax. I would suggest giving them a ring and asking how it will be treated.
That might well be the case. If we start out from the assumption that it is a US Government pension and Article 19 applies the tax treatment comes down to citizenship and residency status.
If the OP is a US citizen then the pension is US taxable.
If the OP is not a UK citizen, but is a UK resident then by Article 19 the pension is not UK taxable. But in Article 1.5b it says that Article 19 does not apply "upon individuals who
are neither citizens of, nor have been admitted for permanent residence in, that State." So the OP is not a UK citizen, but if they are a UK permanent resident (whatever that means) then Article 1.5b makes Article 19 moot and the UK can tax the US Government pension. I have no idea how HMRC assesses residency in this situation or whether it even bothers to apply the saving clause.