How much cheaper are train tickets when buying in advance (UK, Manchester)?

You can use the website Brfares to look up the price of all available tickets between any two stations in the UK. Remember that many tickets have specific exceptions and it can be hard for you to find the cheapest options. In theory, an advance ticket can cost from £18.60 to Newcastle and must be bought by 18:00 the day before departure. Advance fares from £23.00 are then available until 23:59 the day before departure. Both of these types of tickets have limited availability and could sell out before these dates. Whereas, an anytime ticket bought on the day will be £71.00.

You could also look into airport advance these are only available in limited quantities and need to be booked in advance, they are also only available on some routes, but that does include all of your three possible destinations. Airport advance tickets are a special subset of advance tickets which do allow you to change trains without cost, however, they are not as flexible as anytime tickets. You can only get a later train if your flight is delayed, if you are held up at baggage or passport control then you will need to buy a new ticket. You also need to go to the ticket office who will verify your ticket and mark it so it is valid on the later train. You can also only catch trains upto 3 hours after the scheduled departure.

If you go to National Rail Enquiries and ask it for a ticket today (and perhaps next Monday - weekday pricing can be a bit different) you should get a good idea of the probable walkup pricing for any route.

Any "advance" ticket is only bookable in advance (as the name suggests) - tomorrow morning you could can get a single Manchester Airport - Newcastle for £36, but you would have to be on that specific train. Advance ticket pricing often varies depending on exactly which train you are booked on (poking around I could get it as low as £21 on some days/times)

The standard option if you buy it at the station will either be "Anytime" or "Offpeak", the latter restricted to only off-peak trains (with an often opaque way to determine what's peak). These are the "normal" ticket options. However, many lines do not sell offpeak singles, though they are available in some specific cases.

In this particular case, the system is reporting that an anytime single to Newcastle is £71, an off-peak return is £86. This price does not vary depending on day or time (though there are restrictions on when you can use the return ticket). An anytime return would be more expensive still.

Short answer: in this case, "anytime" is indeed apparently the cheapest option for walking up and buying it at the station if you only want a single ticket, no return. One thing I would recommend is running the prices for various stations - many of the Newcastle trains stop at Durham and it's about £10 cheaper, for example.

There isn't really such a thing as "a ticket for the next train". Tickets sold on the day will generally be either "anytime" (valid on any train) or "off-peak" (restricted from some peak time trains, details of the restrictions vary). Off peak and anytime tickets are not limited in number and will be the same price whenever you buy them.

Advance tickets can be significantly cheaper than regular tickets, but you have to book them in advance (generally at least the day before, on busy trains sometimes weeks in advance) and you are locked in to a specific train. There are often multiple prices of advance tickets for a given train with the cheapest ones selling out first.

Looking at Manchester airport to Newcastle and assuming a single journey standard class advance singles vary from £18.50 to £36 while an anytime single is £71.10. There does not seem to be an off peak single available.

So basically you have to decide if a saving or £40 or so is worth hanging around for ages waiting for your booked train.

Finally note when it comes to off peak and anytime tickets returns are usually considerably cheaper than two singles. So the savings from buying advance tickets are often much smaller if you intend to make a return journey.