Any question answered...

I bought them with a debit card, but I have made a claim through Barclays having hit a brick wall with the company I ordered them through - never want to use them again...

But I was just thrown by the wording in the letter from Barclays. Why have they given me the money back, potentially just to take it away again? I'm hoping to leave Barclays soon anyway and head somewhere more ethical.

You purchased the tickets by credit card?

If so, Barclays have equal liability as the retailed under section 75 of the Consumer Credit Act.

Should the retailer fail to provide the goods / services that you paid for, it is often easier to get your money back from the credit card company, rather than the retailer. (The credit card company will likely go after the retailer themselves, with a much bigger stick, to recoup their loss.)

Most credit card companies will have a standard process for this, with form letters and "investigations".

As the consumer, your best bet for the moment is to stick by your guns and don't let the bank fob you off with excuses from the retailer.

Your last resort is the courts, but it's unlikely to get that far.