1. Contact BA, they may be able to help.
As per their UK T&C of carriage:

3e) Your rights if you are prevented from travelling by events beyond your control

If:

• you are a consumer.
• you have been prevented from travelling by events beyond your control and
• all or part of the fare for your ticket is non-refundable.

we will give you a credit for the non-refundable part of the fare. We will do this if you:

• have a completely unused ticket
• have told us promptly about the events beyond your control and
• have given us evidence of these events.

The credit can be used for future travel on us by you or any person you choose. We may take a reasonable fee from the credit to cover our administration costs.

Failing that:
2. Contact your travel insurer

This is one situation where unfortunately you may have to GANFYD, and you will very possibly have to pay for it, but speak to BA first.