Unfortunately it seems like the situation involves too many parties here in addition to things being to clear (are those paid or award tickets, when you say « with ba » do you mean that the tickets were bought from ba or that the flights were ba coded but operated by ei etc?)

in essence, if you had a ba ticket and flights were cancelled in advance, the best thing to do was to contact ba not ei for re accommodation and then everything would resolved. If the cancellation is last minute then indeed you would take this with the operating airline but then if you choose the refund they have to calculate the value according to an established (Mennens) formula not based on the individual cost the segments were priced at and they do not need BA’s input for that.

See main thread on ec261 for details.