How can I refer it to an adjudication scheme when one side refuses to enter a discussion?
Erm.... that's the very reason such a scheme exists.
It gives you, the consumer, an additional form of recourse that is a lot cheaper than taking them to Court.
I quote from the CISAS website :
Before sending your dispute to us you need to have complained to your company and given them a reasonable chance to fix the problem. If the company tells you in writing that they cannot do that or if 8 weeks has passed since you complained to them, then you can use CISAS.