It sounds absolutely horrible, but unfortunately based on the information we have I don’t think any of us will find a magic solution here and a key question is what you are trying to achieve and whether it’s doable.

id first try call Ba again and ask for an explanation and/or tell them what you want. This will at least provide some traçable recorded conversation if need be. Then there are things that are probably easy to achieve and things that are not.

- if your priority is to travel and see your mum, you may ask them if they could reinstate the ticket for agreed new dates. I suspect they won’t do it (in fact it would likely mean creating a new ticket) but if the cancellation was in error that’s a blatant breach of contract and their technical limitations are none of your concern and if it comes to that none of a Court’s concern.

- if your priority is to get your money back and make your own arrangent, I’d write to complain you were denied boarding whilst I’m possession of a valid contract, seek a full refund +uk261 compensation for £520. You can then buy a new ticket.

- otherwise, if your losses were more and you care, this looks looks like a breach of contract on their part so you may be able to sue for the costs truly incurred (eg if you buy a new ticket and it costs a lot more, if there were fees to change hotel booking etc) so you can be whole, but I’d seek legal advice before doing that and bear in mind it will take time and energy.