I note lots of members here are stating that this "instruction" has no legal standing, but:
Do you mean the general instruction which obliges someone to actively go and find the guard? Or the specific instruction mentioned in the original tweet in this thread? Or the sign at Chester?
1) Has it ever been tested in Court?
Let's get back to basics. The Regulation of the Railways Act states:
If any person—
(a)Travels or attempts to travel on a railway without having previously paid his fare, and with intent to avoid payment thereof; or
(b)Having paid his fare for a certain distance, knowingly and wilfully proceeds by train beyond that distance without previously paying the additional fare for the additional distance, and with intent to avoid payment thereof; or
(c)Having failed to pay his fare, gives in reply to a request by an officer of a railway company a false name or address,
he shall be liable on summary conviction
Railway Bylaw 18 states:
In any area not designated as a compulsory ticket area, no person shall enter any train for the purpose of travelling on the railway unless he has with him a valid ticket entitling him to travel....
No person shall be in breach of Byelaw 18(1)... if:
(i) there were no facilities in working order for the issue or validation of any ticket at the time when, and the station where, he began his journey; or (ii) there was a notice at the station where he began his journey permitting journeys to be started without a valid ticket; or (iii) an authorised person gave him permission to travel without a valid ticket.
The National Rail Conditions of Travel essentially repeats these, with a bit more info about what to where Permit to Travel machines are installed, and also clarifies that anyone with a disability who cannot access the facilities is able to travel without a ticket. It then goes on to state that if any of the above 3 conditions apply:
In these cases, you must, as soon as you are reasonably able, buy an appropriate Ticket to complete your journey. The price of the Ticket you purchase will be the same as if you had bought a Ticket at the station from which you first departed. This means that you should buy a ticket from the conductor on the train if there is one available; at an interchange station provided there is sufficient time before your connecting service; or, if neither of these is possible, at your destination.
And that is, to the best of my knowledge, it in terms of what the law has to say about ticketless travel.
From this, we can add one further clarification. Railway legislation rarely goes beyond Magistrates Court and as these don't set precedents, then there is rarely anything set. There are a few precedents but the main one cited in relation to paying once you've started travelling in relation to the Regulation of the Railways Act is Corbyn v Saunders (1978). But you can see the summary of this in the Weekly Law Reports here:
If a person, when travelling, intends to travel beyond the destination of the fare paid, he travels the additional distance with intent to avoid the required payment therefor; and if he fails to tender the outstanding balance of JJ the fare, at the latest, when passing the ticket collector on the station of destination, the requisite intent to avoid payment within section 5 (3) (a) is proved
So Corbyn is only useful in determining that intent is proven when passing an opportunity to pay at the arrival station, although it has also been cited I think to support the argument that intent is shown where someone has passed an opportunity to pay when boarding too, and I think that's a reasonable argument. What it doesn't really get into is anything about buying on the train itself.
2) Can someone point me to the EXACT part of the various Acts that states it isn't allowed?
As rs101 says, the question doesn't seem to make much sense. If the law doesn't state that you need to find a guard, then, you do not need to find the guard. There doesn't need to be a sentence saying "you don't need to find the guard".
The only scope really for argument is in terms of that statement in the NRCOT that "you must, as soon as you are reasonably able, buy an appropriate Ticket to complete your journey...This means that you should buy a ticket from the conductor on the train if there is one available" What counts as 'reasonable' or 'available' is not defined and can probably only be ascertained situationally. As has been said, it would be unreasonable for someone to seek a guard on a standing-room only 12 carriage train. And it would be unreasonable to ignore a guard walking down a train saying "anyone needs a ticket". What happens in cases which fall between these binaries would come down to an argument in court, but what can't be said is that all passengers must always seek out the guard.
In terms of the instruction at Chester and the Tweet: the law permits notices at stations or "an authorised person" to give permission to travel without a ticket, but it doesn't give either those notices or people the authority to demand that a ticket must be purchased on the train. Therefore I don't see how those specific instructions can carry legal force to oblige you to buy on the train if you are not reasonably able to do so.