I think the arrangements at the actual crossing in question have been answered.
On the general question though, he’s what I have to say...
Phones intended for pedestrian users at level crossings are quite unusual but not entirely unheard of. Generally if there is limited sighting for pedestrians the mitigations used are whistleboards and/or miniature red/green lights. Phones are really intended for vehicular users or those crossing with animals onnthe hoof (e.g. sheep, cows, horses etc)
The NR helpline is contracted out to an external call centre company so they can’t deal with stuff in real time, they just take the details, prioritise it and pass it on but that can easily take anything from an hour upwards to get to the right people.
There are basically three categories of level crossings.
The first is a level crossing provided for a public road or similar. Because these are regularly used, they get the most attention and the most money spent on them. Hence normally you get the amber and flashing red road lights (wig-wags) type ‘traffic lights’. Most also have barriers.
The second is where there is a right of way, but the land on at least one side of the railway is privately owned. These are accommodation crossings. They may include footpaths that the public can use. If the crossing is a pedestrian only type and the sighting distance is good enough for the line speed of the trains, then all there will be is a sign. No telephone or other communication or other equipment will be provided. If there is insufficient sighting distance, then normally a direct line telephone (to the controlling signal box) on both sides of the line will be provided. If telephones are provided, in most cases no other form of communication or other equipment will be provided.
If the accommodation crossing is for use with vehicles or animals (sheep, cattle etc.) then it is more likely to be provided with telephones as described above. Crossing users must follow the instructions on the signs. But with most of these crossings, if the sighting is good enough, a pedestrian (who has no physical disability) is not required to telephone for permission to cross. However any user who will take a vehicle, animals across, or where a longer time than normal will be required to cross, they are required to contact the controlling signal box (normally by the direct line telephones provided). The signallers instructions should be obeyed. Please note that not all these crossings have telephones. If the sighting is not good enough for pedestrians, then you should not cross until the signaller has given permission.
If the accommodation crossing is a busy one, the sighting of approaching trains is poor, or there is a history of crossing misuse, then level crossing red/green lights may be installed. Telephones are often still provided so that users with slow moving vehicles or animals can get permission from the signaller.
The third category is crossings provided for railway staff and sometimes for passengers.
As well as the above arrangements, there are other variations such as electricity operated gate locks.
A crossing near me is on a public bridleway, it is also a farm crossing. There's a telephone, and from memory an instruction to use the phone if crossing with animals - i.e. if you're moving a herd of sheep. That doesn't apply to people crossing on their own, and presumably crossing with a dog (and there are other crossings nearby which don't have a phone), I'm not sure if horse riders have to use the phone or not to cross, and if they do what happens if they can't use the phone.
A dog on a lead (or a well behaved dog not on a lead) is not considered to be a farm animal. It’s all about how long it takes for the person, people, vehicle(s) or animals to cross over the line(s) and how much sighting distance the user gets of any approaching train.
Would the ability to communicate with Network Rail by some sort of text message on your own device be a reasonable solution? OK, it's a bit weaker safety-wise because they know where the crossing phone is but they would be relying on someone relaying where they are accurately, but that could be resolved by giving crossings "names" that are tested to ensure e.g. predictive text doesn't corrupt them to the point of being potentially confused with another one? Or using crossing numbers that contain a strong checksum so if mistyped it can't lead to them thinking it's another one?
There should be an alternative number provided at all public crossing phones.
Each crossing in a signal box area should have a unique name and a OS Grid Reference number. I don’t know if it is now a requirement for a telephone number to be provided. But normally an alternative telephone number is provided so that if the direct line telephone does not work, a user can report this.
Once again I’ll make the point that public level crossings where pedestrian users are required to phone the signaller to seek permission to walk across are very rare. The telephones at user worked level crossings are typically only intended for those users crossing with vehicles or animals on the hoof. There is nothing to prevent a pedestrian phoning the signaller before crossing but equally there is no need for them to do so in order to use the crossing safely.
The vast majority of crossings which cater for pedestrian users will either be entirely passive (i.e. no additional warning mitigations for them at all) or will have some combination of whistle boards and/or miniature Red/Green lights to warn the user of an approaching train. All user worked, bridleway or footpath level crossings have signage telling the user how they are supposed to use it - even just a basic ’Stop Look Listen’ sign at a passive footpath crossing is an instruction on safe use.
The elaborate hi tech text messaging, CCTV systems etc.. devised here are really solutions in search of a problem.
CCTV systems are only used for level crossings where there are full width barriers across the road. As they require both more infrastructure and there is a limit on how many CCTV crossings a signaller can supervise in addition to their other duties.
Note that a lot of railway line side telephones (including level crossing telephones and operational ‘phones such as SPTs) include as standard, induction loop technology that works with hearing aids.
If a regular user who has a disability will be using a crossing regularly, it is worthwhile contacting Network Rail. They are well aware of the law regarding disability. It is possible that an suitable alternative could be found.