From the Terms and Conditions, which by continuing use of the site and purchasing you implicitly accept:
Chain Reaction Cycles disclaims damages of any kind, compensatory, direct, indirect or consequential damages, loss of data, income or profit, loss of or damage to property and claims of third parties implied or otherwise relating to use of this site.
You’ve done well to get a refund on the tyre as they could easily argue that something had caused it to split/puncture.
Sadly in this country, people think they are entitled to “compensation” in some form or other for everything.