Hi Gordon,
The pension provider is required to deducted tax in every case, until such time as HMRC issue code NT.
We can only issue an NT tax code or refund any tax paid, when we have proof you are tax resident in the USA.
The only accepted way to prove that you are tax resident in the USA and not taxable on your UK pensions, including state pension; is by completing the DT individual form at:
Double Taxation: UK-USA (SI 2002 number 2848) (form US-Individual 2002).
The completed form is submitted to the IRS (see the notes for the address to send it to) for the IRS to confirm that you are tax resident in the USA. They will send the validated form to HMRC for processing.
We do have a backlog of post, so it may be a while before your claim is processed.
Thank you.