Not running the trains should hurt the company's reputation though. But the problem is that due to decades of propaganda, the companies have successfully managed to convince the public that train unions go on strike for frivolous reasons, or even just to get some time off. At least that's the issue here in France.
Also idk about UK law but in France, the employees refusing to check tickets would be committing a crime, and we already have better laws regarding rights to strike than most of Europe...
I think they would do that if they could - my understanding is that kind of action is illegal. This is ultimately the result of legislating against all other forms of protest.
The train guards are the ones who check the tickets, do the announcements etc. the drivers went on strike a few years ago (and maybe partially now too?) to stop them being fired. They can't run trains without them.
If the law is anything like what we have in France, the inspectors are indeed allowed to strike. Which means, not showing up to work. If they are not striking they have to do their job.
And refusing to inspect tickets in this situation would be grounds for termination for "serious misconduct", because it's an explicit breach of their contract, and also a crime if the company says it has cost them more than 1000€ (not sure about the sum but you get the idea) because it would be considered as defrauding the company