A ticket is a ticket is a ticket. How you pay for the ticket does not affect your rerouting in IRROPS, whether that is strike, weather or mechanical.
BA will either reroute you in the same class of service or let you wait for the next service which has availability in your ticketed cabin. If the former, you are all set. If the latter, you have to make a decision as to whether the downgrade is acceptable. In addition, if you choose to wait, BA has no "duty of care" obligations under EC 261/2004, although it is not unheard of that it will nonetheless take care of you.
If you are downgraded, you are due a refund of your 30-75% of your base segment fare depending on the distance covered by the downgraded segment.
The real key here, as with all IRROPS, is to be armed with information as to what you want and not to passively stand there and be handed new boarding passes. If you have done the research, you are then in a better position to ask for what you want.