For some background investing as a US citizen living in the UK:
https://www.bogleheads.org/wiki/Investi ... _residents - recommend reading this first so all the terms and acronyms below make some sense!
I think the big one you're missing is a UK SIPP (self-invested personal pension). Assuming you can satisfy yourself with respect to the whole "foreign grantor trust" question, and thus forms 3520/3520A and potentially PFIC considerations, a SIPP would be an ideal vehicle for long-term tax-advantaged investing (sorry for throwing all the acronyms and obscure terms out there - SIPPs have a bit of grey around them where there's no clear consensus. Talk to your accountant, assuming they're dual US/UK qualified). £40k annual limit (with rumours that the Budget being announced today will increase that), tax-deferred until withdrawal by both the US and UK, generally quite similar to a 401k, except you don't need an employer.
When you say "set up a self-employment", you're already a freelancer and thus self-employed? But in relation to a SEP, what I think you/your accountant is saying is that you'd have to set up a company and you'd be the only employee? In which case yes, I agree that adds a lot of complication, especially when you talk about US citizens owning UK companies.
Traditional IRAs also get into some questions - would you be looking to deduct the contributions from your UK income tax? If so, a close reading of the treaty implies that the IRA would have needed to be set up prior to leaving the US. If you don't deduct from your UK taxes, you're paying after-tax money in there, but will still get taxed on the growth at withdrawal - need to keep good records. Not worth the effort for a $6k limit, to me. But one key advantage could be the ability to get around the catch-22 of PFIC and KID/KIID, since you can just buy PFICs inside the IRA.
The other semi-advantaged option is an ISA (UK tax advantaged, but US taxable). Today, it's a pain because of that PFIC + KID/KIID catch-22. But hopefully soon (fingers crossed!) the UK will repeal the KID/KIID requirement, in which case you could easily invest in US ETFs. £20k annual limit, UK tax free on capital gains, dividends and interest (basically the same as a Roth IRA, but without the age limit on withdrawals - withdraw any time). Does have to be reported as a taxable brokerage account on US taxes.
Bit of a conundrum on the ISA since the UK tax year ends on 05Apr, and I don't know if we'll hear about the repeal of KID/KIID before that (I'm hoping it's in the Budget today, but that's just a hope). You could fund an ISA in the next few weeks with £20k, and then do another £20k after 06Apr. If/when KID/KIID gets repealed, you invest in appropriate US ETFs. If not, you could either do individual stocks, or just leave in cash while you wait (although the interest rates may not be great - probably better at Interactive Brokers than Hargreaves Lansdown, the two main options for US citizens).
I know that's a lot to throw out there, happy to help with any questions to the best of my ability (I'm not a professional, just a self-taught amateur, but in a similar situation - I'm a US citizen employed in the UK with a self-employed EU wife, albeit with an un-surrendered green card, so she's in the US tax system too).
