Hi all. New to the forum and looking for a bit of advice before I pursue legal remedy for an ABS pump I had supplied and fitted by a local garage which turned out to be faulty. It's a fairly long story so please bear with me!

I noticed problems with the ABS system in my '04 Octavia at the start of last year. I took it to the main dealer who diagnosed a faulty pump, quoting me around £1500 for the repair. I shopped around for a better quote a garages I'd used previously and went with the best one I found.
The car went in and the pump was changed but unfortunately the problem remained. Diagnostics were unable to identify any further issue but the garage suggested they try a few other other things. More parts and labour later, still the original problem persisted and the bill now stood at over £1200. The only option remaining, according to the garage, was for them to take car off my hands, for "scrap", in lieu of payment. I politely declined and reluctantly settled the bill in full.
I took the car back home (Czech Republic) to an authorised Skoda mechanic along with the original diagnosis. There they replaced the pump again and lo and behold, problem solved! I informed the garage in the UK of the situation and asked for a refund, for the pump itself and additional work carried out as a result of them fitting a non-functional part. After much correspondence, they finally agreed to send the part back to their supplier for testing. Last week came word from their supplier that the waranty was not to be honored for the following reasons and that there was nothing more to be done (copy and pasted verbatim):
1. Part to replace faulty unit could have been done by dealership in Europe
2. Parts warranty cannot be done now as it is off vehicle & (name of supplier) can not authorise for electrical items
3. All warranty above £100 must be taken to relevant dealership.
Regardless, my agreement is with the garage who carried out the work, not their supplier and I believe they are liable under the CCA, as they sold me a non-functional unit. Of course, no one wants to accept responsbility but I am prepared to take pursue legal action as this has caused me a lot of time and money.

Does anyone have any advice how the CCA may apply in this case, what my options are or any other relevant information?

Thanks in advance.