PAYE and the Foreign Tax Credit
Income tax withheld at source under PAYE, plus employee National Insurance, generally exceeds the US tax on the same salary. Form 1116 credits it category by category, and the residual US tax on employment income is commonly zero.
Your P60 and payslips are the cleanest evidence of UK tax actually withheld — exactly what the credit needs, once the April–April period is split to the US calendar year.