Trainspotters do need to inform the station supervisor that they intend on doing some trainspotting and also take photographs in this country
They don't *need* to, it's a common curtsey, since it is their property, but the default state in the UK is that photography is allowed unless otherwise sign-posted, or informed, even on private property.
That's to say, if you DON'T ask, they can get mad, and ask you to leave their property, without extending any kind of option of you doing so within their limitations. But they have to tell you to stop, or post signage that says 'no photography'. Of course, more likely they just call the police rather than deal with any confrontation themselves, and the police are woefully ignorant on the 'rights' (actually, no rights, just a lack of laws) concerning photography - so much so that the heads of the police forces have had to send memos to their employees several times over the last 10 years.
Either way, it's not a 'crime', since the only possible bad thing to result is that they can bring a trespassing case against you, which is a civil act not a criminal act in most of the UK (Scotland has trespassing as a criminal offense, but they're weird anyway

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But yes, if you ask, then they're likely to grant you the ability to take photos, at least at the smaller stations, the bigger stations tend to be managed by feckless idiots that are unable to think of anything on their own.
(Many of the big stations have 'no photography is permitted' signage anyway)
Now, again, I specifically kept off of the station (which is non-staffed, and doesn't even have a ticket machine), and remained purely on the public right of way which I have every legal right to take photographs from (since there isn't a military base within about a dozen miles of here), in the situation I mentioned earlier. If the driver in question had reported it, it would likely have resulted in a visit by the hi-vis thugs without any station staff on hand (and may have anyway, since the police are so poorly trained in this area that they'll happily dispatch some to confront you, even threaten and intimidate you until you get them to talk to someone at their station that actually knows the law or is able to read.