Sorry if this has been asked before, but my regular train is timetabled as standard class only. However there is frequently a first class compartment due presumably to Thameslink not giving a monkeys.
Yorkie has already given a detailed reply, including a thread I posted in 2009 giving an example. However, I felt like replying to say that Thameslink isn't 'not giving a monkeys' by occasionally running trains that have first class when it isn't offered on that particular service.
It happens as stock is moved/swapped around, and indeed this will often be why some services don't have first class - because there's a chance that some trains will be without first class accommodation. A good example is many peak semi-fast trains on Great Northern. Usually a 4 or 8 car train with first class, but sometimes a 6-car train without. Thus, it NEVER has first class offered.
AGA also run a number of trains to/from Hertford East and none of these have first class, but the majority of trains will be Class 317s with it, over the odd Class 315 without.
What I would advise is that you carry a pocket timetable with you so you can easily show any RPI that it isn't marked as conveying first class. But then bear in mind that many RPIs don't work specific trains, but simply get on/off as required and fill in log sheets later. Thus, it's always possible they won't even know what train they're on - especially if it was delayed for any reason.
Over the years, and certainly since my post, I've never had any serious issues. As in, I've always convinced staff that I'm okay. To date, I've never been given a penalty fare.
That said, I use AGA quite regularly now and have not yet (in about 8 months) ever seen an RPI on a Hertford East train, so have never found myself having to convince anyone.