BA can't simply regard EI simply as a feeder operation for its own services. And as bjghi3 says, if they're upset now, wait until the Open Skies agreement come through . . .
It is strange (if it's correct) that BA would object to this, in that it has always appeared that the reason BA has switched to smaller aircraft on almost all flights (319s/320s on s/h, 777 on long) is to focus on London rather than being reliant on interlines. Aer Lingus has, traditionally, had pretty poor European connections, but as it rearranges itself, this can only grow and one hopes that the extension of services won't be confined to Europe.
From EI's own viewpoint, it surely makes more sense to fly to these destinations itself, rather than interlining pax, which results in a lower yield. EI is actually reducing the number of 321s its flying to LHR, as more of these are used on flights to AGP, AMS, etc. And as it develops more routes and this reliance on LHR as a connecting hub is reduced, surely this will continue.