IMHO.....as a total know-not-much-at-all layperson, only if you to the a credit for UK tax paid to offset US tax.
But if your only income (like mine) is US SS and a miniscule amount of interest, you likely had little/no US liability anyway. In any case, unlike a state tax refund the entire amount would not be reportable - remember you itemize and deduct all the state tax; you don't deduct all the UK tax in the same way.
Seems like if you did claim a credit, then it's just a matter of filing an amended return, allocating the 'refund' to the US calender year w/r/t the credit you took (if any).
Some professional will likely jump in now with some complicated answer....