Like Durhamlad, I'm presuming your wife is a US citizen. I'm also presuming she has no after-tax contributions in her 401k (only pre-tax salary and matching employer contributions) .
Also a reminder that we're all self-educated self-help group around here as you dig deeper into things, you may find reaching out to a tax professional is worth the cost for peace of mind and tailored advise.
Step 1 is to roll over the 401k to a traditional IRA and open a Roth IRA within the same provider for Step 2.
Rolling over the 401k to a traditional IRA is not mandatory - you can make conversions directly from a 401k to the Roth IRA if you so desire (it's still a taxable event though, and the math is unchanged). However, unless your 401k is (a) with a large international employer who is used to dealing with international ex-employees, and (b) with the same provider your Roth IRA is/will-be with, I personally would roll the 401k over to a Traditional IRA first.
I would recommend making opening the Roth IRA the very first thing you do, before any of the other stuff.
This is exempt from taxes in both countries but it has to be reported as a non-taxable event when filing your tax returns in the States.
Yes, the rollover from a 401k to Traditional IRA is not a taxable event
when done correctly*.
It does NOT need to be reported in either the UK or US tax returns (short of putting something in a comment box somewhere, I don't think you could even if you wanted to).
* i.e. it's actually executed as a direct rollover. MAKE ABSOLUTELY SURE THE ROLLOVER IS EXECUTED AS A
DIRECT ROLLOVER. A direct rollover digitally moves the contents across. Otherwise, they just issue you a cheque. You only have 60 days from issue in which to get that cheque into the Traditional IRA before it gets considered a withdrawal (which is (a) taxable and (b) can no longer be put back in a retirement fund). 60 days sounds a lot, but it's not if international postal times are involved or there's a problem. If something goes wrong and you get a cheque, whatever you do, DO NOT CASH IT. Even if your intent is to immediately transfer the money from your account into the IRA. The cheque itself has to go to the IRA plan administrators. If you do anything else with it, it magically becomes a distribution - a taxable event that no genie can put back into the bottle.
The vast number of people never have a problem with a rollover, but the consequences of it going wrong are bad so you want to watch the process like a hawk.
Does my wife need to submit a self-assessment on the back of this in the U.K.?
No (unless they issue you a cheque which you don't deposit in the Traditional IRA as noted above).
Step 2 is to start converting the IRA amount to Roth IRA which adds to your taxable gross income but as she’s unemployed we could convert less than the standard deduction per year and not pay any tax. As far as I understand the standard deduction for married people filling separately is $12,550. So as long as we stay under that amount we won’t pay any taxes.
Married Filing Separately (MFS) is a slightly odd beast as for couples with equal incomes it shouldn't make a difference and for couples with unequal income MFJ should always result in less tax than filing separately. A typical use of MFS for example is when one partner doesn't want to sign off on the finances of another (due to fraud, undergoing divorce, etc). The other, as I think you've found, is when a US citizen is married to a non-resident alien (NRA).
In an earlier reply I said
typically you wouldn't need to file a tax return if you were under your deduction, and gave a link to the full rules. Unfortunately, one of the exceptions listed in the full rules is MFS - I guess they really worried about US resident couples hiding partner income. As a result, the worldwide income threshold for having to file a US tax return when filing MFS is a miserly $5 (yes five whole dollars!).
It's not something I've looked into, but I would expect as long as she stayed under the standard deduction, it would still be zero tax.
However, depending on your (not hers) circumstances, you may want to consider filing jointly, even if you are a non-resident alien (NRA) who otherwise wouldn't be involved in the US tax system. According to this article:
https://www.americansabroad.org/nonamerican-spouse-us-tax-implications/) you can opt in to being taxed by America. Then the first $108,700 of your UK salary could be completely offset by the Foreign Earned Income Exclusion and your wife could then take advantage of the $25,100 Married Filing Jointly standard deduction.
If you go this route, you'd definitely need to get a tax professional to validate the plan and to prepare (at least the first year) of your US tax returns. Some UK investments that would otherwise be safe for a NRA to hold became a reporting and/or tax inefficient on US returns, so that may be a showstopper. Specifically ISAs are not tax protected in the US. PFIC stocks (mutual funds etc) are taxed very heavily by the US, and are so difficult to report, US tax preparer charge thousands of additional dollars for returns that include them. These are all problems a US citizen living in the UK has, so your solution would be the same as your wife's: Don't have these sort of savings :-) (sell them before the start of the reporting year)
Step 3 is to withdraw the funds when she’s over 59.5 as a lump sum which will not be taxed in neither US, nor U.K. A bit confused here - if you withdraw this in chunks, it will be taxed in the U.K.?
No tax to either country, provided the money you are taking our has either been in the Roth IRA for at least 5 years or is the result of growth from money originally invested at least 5 years ago. How often and how much you take out at a time doesn't matter.
You are probably already aware of your wife's FATCA and FBAR reporting requirements, but if your currently under the reporting limits (unlikely) then piping a meaningful lump sum withdrawal through UK bank accounts will put you over.
