If I recall correctly, I cancelled an Avios booking on 1 July using the system, received an e-mail 4 July saying we're refunding it, Avios landed 5 July and received the refund to my card on 13 July.

I did not receive any kind of voucher though, so if you have a voucher, I would assume you're not getting an automatic refund to your card.

Nothing happened on 1 July with regards to notification, the only one was 4 July and it said -

Dear MR FLIGHT DETECTIVE

We’re sorry you couldn’t travel on your Reward Flight booking reference ABCXYZ. To offer you maximum flexibility we’ll be cancelling your booking and refunding you in full.

You don’t need to do anything. We’ll automatically credit the Avios back to your account and refund the money to your original form of payment. We expect this to take approximately 4 weeks and it means you’ll be able to use your Avios as you wish, to book a new trip on ba.com or however you choose when you are ready to return to the skies.

If you used a Companion Voucher and/or a Gold Upgrade Voucher on this booking, we will add it back to your Executive Club account with its original expiry date. This will be done automatically by us.

We look forward to welcoming you on board again soon.

Warm regards,
British Airways

So if you didn't get the above and have a voucher instead, I wouldn't bank on getting a refund I imagine.