All the major transatlantic airlines have voluntarily agreed to New York Governor Andrew Cuomo’s request that all passengers have a negative covid test before flying.
British Airways issued the following guidance on its Covid-19 entry requirements page:
“Please be aware that you need to provide evidence of a negative COVID-19 test certificate before you’re able to travel to New York. The test certificate must be issued no later than 72 hours before your departure time and will need to be shown at check-in when you arrive for your flight at London Heathrow Terminal 5.”
If you fail to show a negative test in the required time frame you will not be able to board your flight.
It is important to note that this does not need to be a PCR test. LAMP tests are also accepted.
You do not need a test if you are transferring in New York to another flight.
(EDIT: late on Wednesday, New York also announced compulsory quarantine for all arrivals from the UK.)