Private companies, such as those providing funeral services, can register here: https://www.gov.uk/get-workplace-coronavirus-tests for access to workplace testing. Once approved they will be given access to the Egress portal where they can read procedures, agree to the contract and then place an order for testing. The link provides details of how to access workplace testing for companies with more than 50 staff.
For companies with less than 50 staff, those companies may be able to access local community lateral flow tests by going to https://www.gov.uk/find-covid-19-lateral-flow-test-site to find out more if such tests are available in their area. Alternatively, companies with fewer than 50 employees who would like to know how to access testing for asymptomatic cases in your community, can contact CommunityTesting.CentralOps@dhsc.gov.uk