BA flight issue - where to complain?

[LoveToOat]

Apologies if this is posted in the wrong topic, if so happy to be directed elsewhere.

Briefly I'm after advice on where best to escalate a complaint with British Airways? They have messed up our flight to the States later this year. Rescheduling us on a flight that was far too late (we have very young children). Then only giving us two flight options despite several flight options including our original flight being still visible on their website. We accepted a flight on the belief others weren't available and with assurance in writing by BA that seats were booked only to find out we'd been lied to on both counts - the new flight is also operated by a separate airline who do not allow for seat booking. Several calls to BA asking for a manager to rectify the issue have been met with false promises of a call back. It's been several weeks. Is there anything else we could do?

All ba affiliated airlines offer seat booking. Why have they changed the booking if the original flight is not cancelled?

If they change your flight you are entitled to cancel it rather than accept the change, just cancel it.

@Thelondonone thanks for explaining. I simply don't know. They didn't tell us why they were changed and kept saying they weren't available. Only after my 3 (or 4th) phone call pressing them to check the flights again did they confirm our original flight is again available but they won't let us book it without a manager. Yet no one is getting back to us.

We're not in an ideal position to cancel our flight. The flights are for a wedding of a very close family member. Cancelling and rebooking several months after we originally booked will be extortionate and unfair given the fault is from BA.