[mothered]

Should I say to them that customer service already indicated in an email previously that I would receive a refund?

They didn't state you'd receive a refund, but rather a request was pending "approval" as per below.

I've gone ahead and requested a refund for your order #X. Once approved, please allow within 3 to 5 business days for the amount of £X to appear on your CARD ending in X.

You can still try and dispute It by asking your claim be escalated. Be sure to forward their email to senior management.