Can I make a claim through my bank for a refund not received? England

I purchased some items online for Primark Click and Collect and returned them in store pretty swiftly after.

I asked for a receipt but they said one wasn’t produced but pretty standard and I’d get an email.

No email was received and so I got concerned and 5 days later put an online query form stating the store, time it was returned and said please even look at the cctv (which says it takes 2 days to respond). It’s now a month later and no response, no refund.

I’m not near the store so can’t deal in person, no one answers the phone and I can’t find an email address for Primark.

Can I just do a chargeback through my account for the original purchase? Or what other avenues can I take?