Greetings @britishrob!  This is a great question.

• The payor, or bank that holds your 401(k) will provide you a 1099-R  for the year that distribution is made.  You would report this on your income taxes.  Note that your entire withdrawal will be taxed as US income because the contributions to your 401(k) are made with pre-tax dollars.  
• You would only need to file US  income taxes when you withdraw the funds. 

Here's a great article to review that provides great information and options to consider for a  nonresident with a 401(k) that is planning to return to their home country.

https://www.investopedia.com/articles/personal-finance/100515/how-are-401k-withdrawals-taxed-nonresi...

@britishrob Hope this helps and good luck on your move!

Hello again, Rob! Great to see you once more.

So you noted you are a non-resident alien, in which case you would need to use Non-Resident tax prep software, this company is the tax partner of TurboTax: https://www.sprintax.com/ 

Many nonresident aliens who live and work in the U.S. choose to invest in a retirement plan offered by their American employers. However, when it’s time to return to your home country, this can create quite a quandary. Should you leave your funds in the 401(k)? Should you cash it out before you leave the U.S. or wait until you’re back in your home country? Should you roll it over into another account? And how will your 401(k) withdrawals be taxed once you no longer live in the U.S.?

As far as income, upon withdrawal the investments would generate income, issued on a 1099-R, and at that point you would need to file a US Tax Return, but not every year. 

Sources:
https://www.irs.gov/individuals/international-taxpayers/nonresident-aliens

https://www.irs.gov/retirement-plans/plan-participant-employee/401k-resource-guide-plan-participants...

https://www.irs.gov/pub/irs-pdf/p590b.pdf

Additional Information for Withdrawals:
https://www.irs.gov/individuals/international-taxpayers/nra-withholding

I hope that helps!