score:2
That's tricky since this specific case isn't covered in the EU261 regulations.
BA will likely drag their feet: on the first cancellation, you got rebooked to a cheaper ticket. On the second cancellation, you are offered a refund on the ticket that got cancelled.
I would try the following angles with the BA representative:
- reimburs*m*nt within seven days, by the means provided for in Article 7(3), of the full cost of the ticket at the price at which it was bought
See https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32004R0261
If they cancelled less than 14 days before departure you are also owed additional compensation.