IB to HF, London. Limited roles available…should I move to NY?

There's no shortage of people who can produce good paper ideas for single-manager funds. Times a thousand if they "apply PE process to public markets" so there's really no incentive for top US SMs to take someone they need to sponsor vs the HSW Blackstone guy.

Large platforms like MLP let you move around, but they are the bulk of funds hiring in London anyway and OP doesn't want to work for an MM.

Let me clarify things as someone who has done this for a similar reason as you. There are broadly two routes for vast majority of people in your situation.

1) Get yourself on an H1B visa.

This visa allows you to work at any company that is willing to sponsor you in the US. Unfortunately, having a company want to sponsor you is not enough. In the US, there is a quota on the number of people who can receive an H1B every year (that’s just immigration policy). There is always way more people applying compared to the number of visas available and the US uses a lottery system to decide who wins the H1B visa. Every incremental year, there is structurally more people wanting to move to the US but yet the quota of H1B visas available have not changed. So the odds of winning one having been coming down from 30-35% to 10-20% now. The question which companies face then is: why would I hire someone who needs a H1B visa if there’s only a 10-20% chance they’ll actually be able to join us because of the lottery? For majority of roles (especially at the somewhat commoditized analyst level), it makes no business sense to do so. Given you’d be applying from the UK with no ties to the US, you can forget about companies/funds considering you seriously.

2) Get yourself an internal transfer (L1 visa)

This is far more promising of a route and only applies to funds with an office in both the UK and US. Basically you join your fund in the London office and then they transfer you internally to their US office on something called an L1 visa which is an internal transfer visa. There is no lottery system here. Your fund just needs to justify to US immigration that there is a pressing business need for you to be in the US because you have a unique skill set in the company that no one else has. To demonstrate that you have this “skill set”, you typically must have been working for that fund in the UK for at least a year before you’re legitimately seen as someone who has acquired enough knowledge about the role in that company that can be applied to the US (basically you can’t do one day in the London office and then suddenly be seen as an asset that can help the company in the US). The catch with this visa is that your L1 visa is tagged to your specific role within the company you are internally transferring with. This is why you cannot recruit anywhere in the US once you move on this visa. If you lose that role, you lose your visa and you’re out of the country. It makes sense given the context of your existence in the country was because you had a specific skill set for a specific role. So if you’re not doing that role, you have no business being in the country anymore. 

So there you go. US immigration is complex with very high bars to entry. I moved on an L1 via internal transfer many years ago but my fund applied for the H1B for me in parallel (Note not all funds do this). I won the H1B lottery in my first try and transferred visas from L1 to H1B. I was then free and able to recruit elsewhere. I imagine that to be your best bet if you want to be in the US.