Thanks for your question
UK pensions ARE taxable, so I am unsure where you have taken your information to suggest they are not, as this is incorrect.
State pension cannot have tax deducted directly from them, so are taken into account, by virtue of a deduction from the allocated personal allowances, so that income is fully covered, without the need for tax deductions, BUt if they are in excess to the personal allowance, then tax is calculated on this excess, either through the tax code being treated as a K (Minus allowances) code - against another source of income, or the additional tax being calculated at the year end, and the additional tax paid then.
And your declaration of the USA social security pension would be declared on the foreign income page, (along with any USA tax suffered on it, if that is the case) , so that it is added into your total income position.
Sorry - yes, you are right.
So if the UK state pension (or foreign version of the state pension) is below the personal allowance threshold, and if no other income is earned from any source then the pension(s) are effectively free of taxes in the UK?