The approved list of test providers for international travel can be found here: https://www.gov.uk/government/publications/list-of-private-providers-of-coronavirus-testing/list-of-private-providers-of-coronavirus-testing

The UK Government’s Test to Release scheme for international arrivals is now live and people travelling into the UK from countries not featured on the government’s travel corridor list will have the option to take a test after 5 days of self-isolation, with a negative result releasing you from the need to isolate.

Those choosing not to take a test when arriving from countries not featured on the government’s travel corridor list must continue to follow the current self-isolation requirements (10 days).