Is there any prohibition on filming on the railway? Afterall its a public place. Yet I have seen TV programs where crews were stopped from filming. Is there anything unusual about LU?
From my understanding, and I'm not an expert, all bar a few of the large stations are managed / owed by Network rail, so not generally a public place. However in general NR like to support the activity of the train enthusiast but like most things it's a two way partnership. They need to ensure your safety and that of the other passengers and staff, but equally respect your desire to document the trains etc. As such it's just courtesy to let the station manager know you are on the platform and where you wish to place yourself. If that is at the end of the platform away form the high traffic area, they may even agree to the use of a tripod. They may also request you sign the visitors book at the start and when you leave. If the station is small and manned by a single member of staff, I tend to do introduce myself to them so they are aware of my presence.
If the photography is going to be used for anything other than personal use and sharing on social media or youtube then you need to acquire a permit to film, which (and I could be wrong) you get from the main train operator at that station. How much that costs, and the restrictions imposed I have no idea.
Also, if you ever get asked to leave a station by an individual then don't kick off. If you have been given permission by the station manager, or it's the station manager who is asking you to leave, calmly explain who said you could video, and ask if there was a reason for the change in permission. If that doesn't defuse the situation, and they insist to leave then do so without making a big fuss. There have been accounts where enthusiasts have gone passed boundaries agreed and ended up being escorted off the station by the transport police !
Often if you visit a station regularly and see the same staff they get to know you and you can form a rewarding relationship so long as you stick to what's been agreed.