As hinted above, this is a rare scenario where the relevant airline has a more generous policy than BA. BA has a 2, 4 and 5 hour rule in respect of flight changes booked through them, and this change delta isn't enough on BA's policies. So if you go to BA they are going to stick to policy and require availability and a £35 change fee. If AY does the change, they would have to line up the ticket revalidation, which may actually happen -even if's a lounge swallowing sweaty palms job at the airport - but you can't assume BA will over-ride their policies, hence the risk is on you, not the airlines.