As you have discovered, if you have zero presence in the US (address, etc.) it is impossible to sign on with a US based agent such as Vanguard. As for the UK and a firm accepting US Persons for investments, the only place I have heard of recently is A. J. Bell. I know nothing about them. I've never used them or even investigated their offerings or whether in fact they do allow a US Person.
https://www.youinvest.co.uk/Those who were with Vanguard prior to moving to the UK are able to maintain that relationship from the UK after relocation here. But, that doesn't help the long term UK resident who cut all ties with the US 30 or 40 years ago (I've been abroad for 39 years).
There are some suggestions for establishing a US presence, some more strange than others. The first is to use the address of a US resident friend or family member as a permanent US address, and utilise a US based phone network. As you may guess, that may come with any number of scenarios,
not all good. Another suggestion I have seen is when visiting the US, go to a UPS Store, provide a local address, and sign up for their Personal Mailbox service. It can include mail forwarding - anywhere (or so they claim). Best utilised in Florida or Texas; otherwise, there may be State related consequences.
https://www.theupsstore.com/mailboxes/personal-mailboxesWe can't sign on with Vanguard or others in the US because we have no US residence; we can't sign on with Vanguard UK or others because we're US citizens; we can't have UK based mutual funds because they're PFICs and come with brutal US tax consequences.
We
can have individual UK based shares, reportable to the IRS, but treated without the unusual PFIC brutality.
Is renunciation of US citizenship a possibility? Otherwise, you're restricted to UK based individual shares, UK based savings accounts, a purchased UK property, or a Cash ISA.
The following is bubbling away in various congressional committees and may surface prior the upcoming US half term elections:
the "SAVING US CITIZENSHIP ACT" (or a name somewhat similar).
It's totally unknown as of now, and exists as a proposal that may come from one congressman in the form of 1 of 4 Bills relating to corrections in the TCJA (Tax Cuts and Jobs Act). My suggestion is to wait for a few months to see if this does indeed surface, if so what it will contain, and does it have a chance of being passed (it's suggested it has bipartisan support). It
may allow for more freedom for investing in the UK (or possibly not!) but it's guessed it will still require yearly US certification and 3 years of past US tax returns filed from abroad. It may benefit some; it may upset others.