To access the official railway data, no javascript or cookies required- use Accessible UK Train Timetables which has the full official data -as up to date as exists for times- but for fares, there are severe problems with the web site for some journeys.
There are now so many ticket restrictions that National Rail and the train operators themselves are no longer able to cope and the railway computer systems may force train staff to sell you more expensive tickets. Note that a ticket price may only cover one particular train booked at one location at one instant!
It is often cheaper (by a tenner or more sometimes) to split your ticket, especially if you can move a portion of the journey out of peak hours, reduce cross county boundary journeys, or take advantage of greater discounts for shorter journies. eg For one particular train from Manchester to Derby, you can save ten pounds by buying a return ticket Stockport-Sheffield and a separate return ticket Sheffield-Derby.
On times, be sure to use "check for updates" or "bulletins" for the most recent information. If it goes wrong, you may need to contact "Passenger Focus" to obtain a refund on an overcharged ticket! The official National Rail (Mobile) website HAS a mobile version but will redirect most devices to the none-mobile site if it doesn't think you really are using a mobile phone. NOT friendly at all. Our railways are a mess.

Enjoy reading Today's UK train delays-and Cleared incidents- note that the 2004 revamp of the site seems to have caused it to miss a lot of serious delays, or report them later. Local North West delays seem almost never to appear. Northern Rail have now ceased their own journey problem reporting entirely but a small relic can be found on this BBC travel web page.

UK Live Departure Boards has the web equivalent of the tv monitors you see at railway stations, giving arrivals and departures in the next few hours. Note the limited and experimental nature of the data. NOTE a train shows as NO REPORT until it passes a reporting point.
The site National Rail expect you to use has EITHER arriving OR departing trains but not both. Use the station name or the three letter code available from the site below.

An alternative format with both arrivals and departures is available from traintimes.org and but you need the absolutely correct station name (or code).
Don't ask traintimes.org when the next train from Adlington is, nor the next train from Adlington Lancashire. You must type Adlington (Lancs).!!! Adlington in Lancashire is ADL. Get the three letter code from the site below:

Station codes - three letter station codes used for example by manual ticket office or train crew machines, useful if you are told they can't issue a ticket to a station. For example in Manchester a ticket to CRS code MCZ (which prints as Manchester CTLZ) includes travel on Metrolink trams from your central Manchester rail station of choice to the city centre. The NLC code is 0451 (sometimes as 045100), compared to Manchester Stations which is 0438.

Railway fares in the UK are a nightmare, and very often the headline price - the one you will probably be charged- is not the cheapest fare available, despite regulations to the contrary. You can also lose a lot of money in penalty fares if you accidentlally get on a train not appropriate to the fare you have paid- and it is very none obvious. While I don't like linking to sites that require javascript, hurrah for a US based website that gives FULL details of ticket restrictions and fares.