If you are living in the US either as a US Citizen, a Legal Permanent Resident (LRP) or in any other non-immigrant capacity (such as someone on a student visa) and you require a UK visa, you will most likely need to submit your application for UK Visa in USA.

There are some occasions or situations where you cannot submit your application for UK Visa in USA. For example, when making your application for UK Visa in USA you will need to evidence your residency in the US , otherwise the UK Immigration office may not accept your application.

Why you may not be able to make your application for UK visa in the USA even though you currently live in the US:

Illegal entrants: If you entered the US illegally, you will not be able to provide the legal status of your residency in the US. Even though you may be able to provide evidence of residency such as utility bills, rental agreements. The UK rules require you to provide immigration documents showing your rights to reside in the US.
Overstayer / out of status : Those in this category may also find themselves in a position where they are unable to provide evidence of legal residency, especially if your immigration legal rights in the US expired many years ago.
Pending refugees/ Asylum seekers: Technically a person applying for asylum is not illegal in the US, however, until your asylum is granted , you may not be able to provide sufficient evidence to convince the UK immigration that you have legal status in the US.

What can you do to convince the UK Immigration to accept your application for UK visa in the USA

The first advice is to appoint a UK Immigration lawyer who will be able to present your case for exceptionality.
You may need to take steps to regularize your status in the US. For example, an overstayer can make an application to adjust their status in the US (example on the bases of their marriage to a US Citizen ) . you can then apply for advance parole to permit your travel abroad while the application is pending.
An asylum seeker can also apply for advance parole .

Why would someone who has no legal reside to reside in the US want to make application for UK visa in the USA .

There are many reasons why a person my need to travel to the UK even though they have not resolved their legal residency in the US. Many times, the situation warrants that they make application for UK visa in the USA .

Emergency situations : examples illness of a family member or a loved one resident in the UK

Love: An asylum seeker who has fallen in love with a British Citizen or someone living in the UK cannot be expected to travel to their hometown (due to fear of persecution) in other to apply for a UK visa

There are many more examples that we can think of, what is most important is to employ the services of a UK immigration lawyer if you find yourself in any of these situations