Just a bit more detail on what I did. I'm not saying what I did was necessarily correct, but it's sometimes helpful to know what others did and experienced - and it puts the information out there so the experts on the forum can shoot me down if I messed up. ;-)
I had two 401(k)/403(b) accounts with two different academic institutions. I am a UK resident and citizen; I am not a US resident or citizen.
In 2017, when I knew I had no plans to return to the US, I started pulling what I thought of as "lump sums" from these accounts. I won't go into some of the confusing interactions I had at the time with TIAA-CREF about definitions of lump sum vs periodic payment, etc., but initially, TIAA-CREF withdrew 30% federal taxes from the withdrawals. Initially, I managed to get a "refund" by submitting a 1040-NR form, claiming exemption in section L of the form and citing article 19.2(b) of the UK-US tax treaty, along with form 1042-S.
After this initially very trying period, TIAA-CREF eventually came round to the idea that I was exempt, I used form W-8BEN to claim exemption, and they stopped withholding taxes from any subsequent payments. On at least one occasion, they actually withdrew 30% federal taxes and after several communications, they subsequently refunded the 30% themselves (I have no idea how they did this).
Separate to these "lump sums," I also started receiving interest from the TIAA Traditional holdings I had, which TIAA calls an annuity; it's ostensibly interest. [I couldn't withdraw these holdings as a "lump sum" due to a restriction in the state of Tennessee's retirement rules on state university retirement funds]. Just this year, I converted the TIAA Traditional holdings to a "lifetime annuity" (which is more like what we call an annuity). Since 2017, therefore, I've been receiving monthly payments from the interest, and subsequently from July this year, from the lifetime annuity.
The relevance to UK taxes is this: I ultimately paid no US taxes on any of these withdrawals (because any amounts withheld were refunded, although it often took some time). I declared all of these amounts on an HMRC self-assessment, under the Foreign Pensions section. Rightly or wrongly, I only declared amounts I actually received in any tax year - I declared any tax withheld in the tax year it was refunded (IIRC). This may or may not have been the correct process, but I calculated that, regardless of whether I declared it in the UK tax year it was withheld, or in the UK tax year it was refunded, it made no difference to any tax I owed to HMRC, so I was able to sleep at night.
From reading this forum over the years, I realise I may have been able to offset the US federal taxes I'd paid, against UK taxes due, but I really CBA (I was working in excess of 80 hours a week at the time), and again I figured the amount of tax I owed/paid between the two countries wouldn't change regardless of what UK tax year I declared it.