If they are British or Irish you can check their Right to Work in the UK through checking their passport or another eligible document. As a company you might want to consider using a Certified Digital Identity Service Providers (IDSPs) to carry out identity checks on your behalf.
If they are not British or Irish they can prove their Right to Work by providing a Share Code or eligible Immigration documents. You can direct them to generate a Share code at https://www.gov.uk/prove-right-to-work/get-a-share-code-online.
If they cannot provide either of these you might need to use the Employer Checking Service.
For further details and advice please check out this page https://www.gov.uk/prove-right-to-work.
You may wish to consult an Immigration Lawyer for to plan strategies around this, complex issues and further assistance.
If you have a question please email questions@richmond-capital.co.uk