Trains in England

Can do either. If you purchase in advance and are willing to commit to a specific time and date, you can get discounted tickets. But those tickets come with restrictions as to refund and change. And you can just show up at the station and buy a tickets. Trains rarely sell out.

The National Rail website will show you schedules and fares for the trains you want. Fares bought well in advance are usually cheaper but commit you to a particular train. Changing that will cost additional fare plus an administrative fee. You can look at fare differences by plugging in dates, starting with "today" and out into the future, to see how much you save buying how far in advance. It's a tradeoff between economy and flexibility. The most expensive way to go is showing up at the station to buy, but for some trains the difference may not be worth worrying about.

On our upcoming trip, we've bought one trip in advance because we know we're locked into a particular date to meet a group. But we'll probably buy other tickets a day or two before as our plans evolve, taking account of weather and other variables. Hope that helps. Our UK friends, soon to wake up, will have better info.

If you buy tickets in advance you will get a discount, but with this you will be limited to the day an time that is one the ticket. Then on the other hand, you could just walk up and buy them when you want them.
It seem like you would be using a lot of time back tracking, I would suggest Liverpool to Stratford-upon-Avon, then Strarford-upon-Avon to Bath, then Bath to London.

My daughter and friend recently returned from England and they saved on rail fare by not only purchasing ahead but also with a " Two Together Railcard " ( does have conditions for use )

Yes, your UK friends are now waking up!

If you walked into Liverpool (Lime Street) station today and purchased a ticket to Stratford upon Avon, it would cost you £41.30 for the 2 hour 37 minute trip with 1 change. (Click details at www.nationalrail.co.uk to tell you the change points. These are often only a few minutes - this is normal as most trains run to the minute). If you advance purchase this route, the price stays the same. But - we don’t want to pay all that! Looking at purchasing a ticket for tomorrow - we can get from Liverpool to BHM = Birmingham (New Street) for £9.50. (If you bought on the day of travel, it jumps to £29). Birmingham New Street is right in the centre of the city. It would be worth having a walk around for an hour or two. Then, purchase on the day a ticket from Birmingham (Moor Street or Snow Hill station) to Stratford-upon-Avon = £7.70. Total cost Liv to Stratford-upon-Avon = £17.20.
http://visitbirmingham.com/#

If you do not wish to visit Birmingham, you should check the times for a journey from LIV to SAV and click ‘details’. This will tell you to change on the outskirts of Birmingham at Smethwick Galton Bridge (SGB). Note the times and rapid change times for the train to Stratford-upon-Avon. Should you choose this option - still purchase (in Liverpool) a day or two in advance a ticket for LIV > Birmingham (rather than SGB). Also purchase SGB > SAV but make sure you tell the clerk the date of travel first.

If you walked into Liverpool station today to purchase a ticket for a train to Bath (today), it would cost you £82.70 for the trip - which is around 4 hours. I just checked for 11 October and the prices are £26.80 to £33.70. So, in this instance, you should definitely pre-book a specific train ahead.

No rail line directly links Stratford-upon-Avon with Bath. Therefore, taking a circuitous route, the trip would take around 3 hours with 3 changes and the price is £59. I would not advise doing this. Assuming that you have gone from Liverpool to Stratford-upon-Avon and then wish to proceed (on another day) to Bath; I would take local bus services via some quaint Cotswold villages. For example, today you could leave Stratford-upon-Avon on Bus 24 for Broadway, Worcestershire. (This bus goes via the lovely small town of Chipping Campden). For timetable > choose route 26 & click MORE.http://www.johnsonscoaches.co.uk/timetables/

Then, you could depart Broadway on bus 606 for Cheltenham Spa, Gloucestershire. Have a look around Cheltenham before taking a local bus for the 1 mile link to the rail station. The Broadway to Cheltenham bus service is here:> http://www.marchants-coaches.com/606-Service

Now, as it would be difficult to perhaps figure out an Advance train to book to Bath, I would just show up and pay on the day. This is likely to cost £14.30 and you just get on the first train that is going to Bath. If a Cross Country express arrives that is heading SW - get on that and travel as far as Bristol Temple Meads - where you can change for another train for the short hop to Bath. The journey from Cheltenham to Bath should take about 1 hour with trains every 30 minutes between Cheltenham and Bristol TM and every 15 minutes from there to Bath. If you pre-booked the Cheltenham to Bath trip, it would cost as low as around £10. It simply is not worth it and having the stress of having to get to Cheltenham station for a specific train.

Pay directly the local bus drivers. If you do not have pre-purchased rail tickets, buy tickets at station before boarding trains - unless boarding at an unmanned station.

Bath to London (Paddington) is cheaper if you pre-book about 11 weeks out.

www.traveline.info
http://www.chippingcampden.co.uk/contentok.php
http://www.visit-broadway.co.uk
http://www.broadway-cotswolds.co.uk

There is one coach a day that does Bristol to Stratford-u-Avon direct with a connecting service from Bath leaving around 14:30 for £25. Although fewer changes than by train ( which has 2-3, and the route via Birmingham requiring a change of stations) it is slower. Maybe worth considering though.

I hope it is okay to post in this thread (which has been inactive for over a week) – I am new here and not sure of the etiquette :)

I just wanted to thank James for all the useful info. I was scratching my head a few weeks ago trying to figure out how to get from Reading to Louth (Lincs.). I ended up taking the London –> Hull coach from Victoria, which, although a long journey (5-6 hours each way), involved no transfers/changes and enabled me to both nap and see some lovely villages along the way. (Similar to Marco's advice about taking the coach; it was simpler and cheaper, if longer.)

The real puzzler was – and still is – the short (27-min) train ride between Reading and London. I was quoted so many different fares, ranging from (I think) £18, definitely £26, and I finally ended up paying £44, for a Reading–London return ticket. I did get my ticket the day before, from a ticket agent & not a machine (there were always lines at those, and I didn't want to hold people up!), but chose a 'peak' ticket to give me more time in London between arriving and catching the noon coach to Hull. Some combination of factors made the return ticket have to be two single tickets, also raising the price.

I am still confused how far in advance one should buy a rail ticket in order to obtain a lower fare. I consider myself fairly savvy about public transport (I lived on the Continent for many years, and have traveled many other places, including taking trains and coaches in the UK since the 1980s), but I am rather stumped by the current wide variety of rail fares! :) I will play around with the National Rail site some more. It is not a big deal; it would just be nice to have an understanding of how the various factors interact!
I guess I am posting in case anyone has some insight, and also because my experience might help someone else.

(as a P.S. – we did rent a car, which was handy for the Cornwall part of our trip. But the first week my husband needed the car for work, and I wanted to go to Louth to see a friend.)