Section 9b3 of BA’s Conditions of Carriage sets out the options that are available to passengers in the event of a flight cancellation:
http://www.britishairways.com/en-gb/...ns-of-carriage
9b3) If we:
cancel a flight;
delay a flight by five hours or more;
fail to stop at your place of stopover or destination; or
cause you to miss a connecting flight on which you hold a confirmed reservation;
you can choose one of the three remedies set out immediately below.
Remedy 1
We will carry you as soon as we can to the destination shown on your ticket on another of our scheduled services on which a seat is available in the class of service for which you have paid the fare. If we do this, we will not charge you extra and where necessary, will extend the validity period of your ticket.
Remedy 2
We will carry you to the destination shown on your ticket in the class of service for which you have paid the fare at a later date at your convenience and within the validity period of your ticket on another of our scheduled services on which a seat is available. If we do this, we will not charge you extra.
Remedy 3
We will give or obtain for you an involuntary fare refund.
We will give you additional assistance, such as compensation, refreshments and other care and reimbursement, if required to do so by any law which may apply. We will have no further liability to you.
As a take it or leave it downgrade is not one of the prescribed remedies, I believe you have a strong justification in challenging BA’s decision; you are at liberty to point out to BA that it did not act in accordance with its own CoC.