Except he wasn't injured on railway premises, he was injured on the road.
He (like I did) probably ended up in that awkward niche of having what looks like a bad injury due to the amount of blood but really isn't that bad. Had he walked in with his arm hanging off I'm sure even the most miserable jobsworth would have called an ambulance for him.
Much of a muchness really. If someone presented themselves at my office with an injury, I would assist them (and would be expected to assist by everyone else in my organisation as the First Aider here).
That assistance may be handing them the first aid kit (or things from it), saying that I can't help but directing them to somewhere that can help, phoning the emergency services if applicable etc etc.
Whilst I cannot tell you what the law is when it comes to injuries sustained off the workplace site, certainly the view in terms of those of us who are First Aiders is that you should help someone regardless of situation as long that isn't a danger to yourself (and if they are a danger to yourself, then the last thing you should do is assault them, and I certainly wouldn't lie to them either!).
How big is the station in question? I’m not familiar with it. It’s more of a slight misdemeanour than a massive H&S breach to be fair. Certain stations are unmanned so won’t have this provision anyway, and although safety should always be taken seriously, nobody is going to die because there is no first aid kit.
It is law that an employer must make First Aid provisions for its employees. That is usually taken to mean provide a First Aid kit and if there are more than a few employees or it is a high risk site, appoint specific people who are trained to deal with anything that comes up. Again - that is law.
Where members of the public are also on the site then it is recommended that First Aid provision is made for those too. I would expect that the HSE would look pretty dimly on an employer whose main business involves having the public on their premises but then refuses to provide any First Aid provision for them.
As for "nobody is going to die because there is no first aid kit" - No. Just no. First Aid kits can absolutely be used to save lives. From things like stemming serious wounds to enabling CPR (thanks to pocket masks and other tools that are recommended to be in one), to helping combat hypothermia etc etc. There is a reason why places legally have to have First Aid provision on site. That reason is precisely because it saves lives and reduces the chances of minor injuries ended up as serious ones.
So as I said - if there was a first aid kit then the member of staff acted against the recommendations of HSE (but not illegally) by refusing to help (and anyone just as myself is free to judge someone who not only won't help when they can, but then lies about it too), but if he was not lying and there was not a First Aid kit, then South Eastern are massively breaking the law by not providing First Aid provision at the workplace.