I suggest you go and get some decent advice from somewhere like Which? (They have a legal service), from Citizen’s Advice Bureau (as has already been suggested) or make a small claim (as has been recommended).
The difficulty here is that you’re asking for advice but being cagey with the circumstances. I’m not sure anyone will be able to give the advice you need without being in receipt of the facts.
From what you’ve said, it sounds like the company has behaved unreasonably …but …we not really understanding what’s happened and it’s only your side of the story.
Either way, I do hope that you can get it resolved. Good luck.
It wasn’t about the cancellation itself. I totally accept the risk of booking a non-cancellable holiday. It’s about the service being different to what is advertised.
DId you pay online? If so if you return within (I think!) 14 days you could be covered through Distance Selling Regulations too, and that might be the quickest and easiest avenue to go through.
Can a transaction be disputed twice? It looks like the bank omitted to mention in the initial dispute that the service delivered was different from what was originally provided, and in this case it seems like a second dispute with this information would be likely to succeed. Maybe start with a formal complaint to the bank saying that they mishandled your dispute, and see what they can do from there? If the amount involved is low enough they might just pay it out themselves out of pocket.
What the bank can do once they get a defence from the other party is send back a counter argument. So essentially it goes back and forth between the two banks.
Ok, so you booked a holiday and then cancelled it minutes later?
To get any proper advice, you need to explain how the service they were going to provide differed from what you expected/was advertised, how long the period from the cancellation to the holiday was and if you knew if the T&C said the holiday was non refundable before you booked it.
If you booked for London and you were given a hotel in Brighton then fair enough, if it’s not far away, it probably says in their terms they can swap you.