Here's what I would do:
I think that BA misled you when not presenting the option for a refund on the website. Their T&Cs Indeed allow for a refund within 24 hours of a ticket being issued but they did not present you with that option.
I would write them a letter before action requesting a full refund on the grounds that they misled you and only gave you the option of obtaining a voucher. Even that process is dubious as it talked about a refund when the end result was nothing of a kind.
The electronic version process for obtaining a voucher is, in my view, the same as calling and being wrongly told that you couldn't get a refund while ommiting the option of a refund within 24 hours. Had this happened over the phone, you'd definitely have a strong case and I can't see why an electronic format should be any different.
If they either not respond or refuse, then MCOL the amount.