Right to care has no time limitations, it's based on need only. If you ask BA if you will get reimbursed they will say no, because they gave plenty of notice. However it you claim afterwards they just pay up. But it's a risk that they will make it difficult or slow to claim. So it's best not to ask. You can see if going via another airport will keep you on time - so typically TLS, MRS, or LYS. Again they will say they won't cover the train fare to these other places, but in reality they will.