How can I verify the identity of a US | UK -based person and prevent *fake identities* from being accepted?
Given that it's possible to fake ID cards and fake social security numbers are created, I need to ensure that all users of my site are US or UK based citizens, and don't have more than one account....
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Information Security Stack Exchange
The problem is with the phrase identity itself.

Technically Possible with History

There is no way to do this without using some sort of biometric verification. Retina scans would in theory be the only way (since you would not be able to replace an eye [2010]). If you were to do something like blood tests, even then in the case of twins they would carry the same DNA. Also blood transfusion recipients can also carry the DNA of their donors. More on DNA and transfusions. This is all provided that some other form of identification was used when the DNA was taken. The only way for this to be fool-proof is at the time of birth when someone in the room is verified taking DNA, a retina scan, and fingerprints at the moment of birth. At the point it's logged, then it can be tracked as verifiable.

This is only the case provided the persons in the room have been tracked and verified in the same way.

If you were to use fingerprint scans they would have to be done in person with another verifiable biometric test because fingerprint scans can be faked with modeling clay. If a follow-up comparison matched the same samples then you could prove that you had the same person, however you could not technically prove their true identity without performing DNA analysis and comparing it to samples from their parents (who would also need to be verified).

Realistically

In-person, 3rd party verification is the only way to do something like this. Every other transaction can be faked. This is the reason that probation officers show up unannounced at residences and job sites to verify that the person they're supervising actually is holding up their end of the bargain. This happens when the person is at the location and when they are not. They will take a photo ID of the person they're looking for and if the person they meet does not match or if the people at the location say "never saw them," it immediately violates the terms of the probation. Even this however can be faked with planning and there are false positives.

By "site" I'm guessing you mean website? Likely you would not want something this invasive to happen to your web visitors, that being said you can look for private investigators and research firms that can visually verify a client and research with the 3rd parties. They will typically perform credit checks at random intervals and visually verify the target. They can follow the clients to other locations and determine if in fact they are residing where they say they are. In government this is handled by foreign intelligence agencies.

For employers

For jobs, most potential employees must provide "verifiable" references. This can also be faked. Without double-checking contact information and doing research to try and verify the information on an application, employers can potentially hire anyone seeking to exploit the company unknowingly.

An example might be someone from Company "A" wants inside information from Company "B". They list Fake Company "C" on their resume with a lengthy employment. They purchase 4 throw-away phones (or IP phones) and list the contacts as fake names. 3 of the phones are used for references. The 4th number is used as the main line for Fake Company "C". After initial interviews the person is hired. Without a follow-up some months after the check there is no way to know whether a one-time verification procedure was legitimate or not. In highly sensitive industries a post-hire verification follow-up should be standard procedure.

Online accounts

With more and more online accounts cell phone authentication is being used since 1. most people do not carry more than one cell phone 2. most people do not share cell phones 3. it will use a different service than their internet connection

This allows companies to call and talk to the person for verification, you can track their location and login when they're required to have a new temporary password for a new device.

The online account companies are not concerned with singularity though. That being said, even this is spoofable because:

someone can carry multiple cell phones

they can swap out sim cards

prepaid cell phones are cheap now as well

Business verfication

We recently updated contact info for several of my clients on Google maps. Google maps calls (outsourced overseas) the contact number of the business on file for verification of the new business address and contact information. This is often a one-time verbal check. If they were to show up in-person to a temporary office for verification, then the business might look legitimate.