Let me complicate matters somewhat.

Under EC261 the operating airline - Aer Lingus - would be ultimately be responsible for a refund. However internally, between airlines, it is the Marketing Airline that physically makes the repayment, Expedia's arrangement is with BA. BA's conditions of carriage are aligned with EC261 and would normally allow for a refund if there was a cancellation, so had you booked this via BA.com then a phone call to BA would have been OK. On the other hand if you had wanted to rebook the service, well, either airline could have handled it. So if Expedia contacted Aer Lingus then it wouldn't surprise me if they said "sure, we can rebook the flight" but would have had trouble doing a refund: it wasn't their ticket. So I wonder if asking Expedia to approach BA would be more fruitful. The email from Expedia doesn't make it totally clear which airline they contacted.

I think the chargeback answer is a good option in due course, but if Expedia objected to the credit card company's action it may get a bit messy. So mindful of any deadlines in this area I would leave that until other options get blocked off. You can also pursue - well - Aer Lingus in court (MCOL) or BA via CEDR as other options, but I think Expedia would be a better place to start.

We get a lot of negative stories about Expedia in this forum.