An employer may be subject to a fine of up to £10,000 if it employs a person without the Right to Work in the UK.
If a person is discovered to be working illegally, the employer has an "excuse" [and therefore a possible defence against prosecution] if they have retained a copy of the appropriate document that was used to demonstrate that the person did have a right to work.
Thus it may be prudent for an employer to make arrangements for the keeping [securely] of a copy of the appropriate document[s], for each of its employees.
If copies are kept, they should be kept in relation to all employees, to avoid any suggestion of race discrimination, say.
The summary guidance "Prevention of Illegal Working", published by the UK Border Agency, will provide further details.