Track laying and planning permission

You don't need a TWO (which superseded LROs) if you don't carry passengers across a public right of way. You do need planning permission in order to make any change of use, railway or otherwise. There are exceptions to this if you already have a TWO and are, therefore, a statutory undertaking.
Of course, you can construct something or make a change of use without getting planning permission- that's not actually illegal- but if the LPA challenge you and take enforcement action, you can be in serious trouble. IF they don't catch up with you, or don't bother and that situation persists for over 10 years, they can no longer take enforcement action and you can apply to regularise the position.
So, it is certainly possible to build a line, operate trains, etc., without planning permission- such cases do exist- but it's a risky strategy.
As to those lines which carry passengers over rights of way without a TWO or the equivalent, I know of three, at least one of which is the result of an "administrative oversight", as mentioned in a previous post. Perhaps that also applies to the others!

 

To state the obvious, the LPA is going to notice somebody your laying a railway track.

 

Indeed! When we started, in 1987, we laid two tracks inside a large, enclosed agricultural building. In order to get a loco and rolling stock into it, the tracks extended a panel length outside. After some weeks, we approached the council regarding planning permission. The Chief Planning Officer visited, was very supportive but said that we had caused his colleagues a great deal of head scratching! Unknown to us, they had hired a plane to do a survey of the area a couple of weeks earlier. They were not concerned with us, only the nearby built-up area, but our property appeared on the edge of one of the photos. They had spent a whole morning trying to work out what the two pairs of lines, with apparent cross-hatching, extending from what they thought was a grain store, were. The moral is, you never know who's watching!