I hope this helps - I had a flight for the first week of April and sent a Direct Message (DM) to BA via Twitter on 3/11/2020. I received an automatic reply:
Please let us know how we can help. We'll need your full name, contact number, booking reference and email address. For Data Protection purposes, please can you also confirm two of the following in the order they appear: • The first line of your billing address and postcode • The last 4 digits of your original payment card • Name one other passenger • Passport number (If in the booking) • Passport expiry (If in the booking) If you have made your booking with a travel agent, please confirm the name of the agent. Please note, due to high volumes, we’re only able to make changes to British Airways Holidays package bookings where the first flight is on or before 14 April 2020. If your British Airways Holidays package booking includes a flight due to depart after 14 April 2020, please contact us closer to your departure date.
I responded with the info and received a telephone call this afternoon from an agent and we resolved my cancellation request. It came in as "Unknown Caller" on my phone. The agent was very helpful and polite and apologized for the delay in reaching out but it was obviously understandable given the circumstances.