score:7
First, be aware that on many routes considered commuter routes, off-peak travel is SUBSTANTIALLY cheaper than on-peak. So this means travelling after 9.30am during the week, or any time on the weekend.
Second, booking in advance helps. A lot. Use National Rail's Cheapest Fare Finder or TheTrainLine to find cheap rail tickets, or if you're very lucky, absurdly cheap tickets on megabus which sometimes has tickets on trains for less than the price of a beer.
Thirdly, if three or more of you travel together, even buying at the ticket office on the day, you can get very often get a group discount.
Finally, you could consider a RailCard, which gets you discounts on all tickets you buy. You'll need to weigh up whether it'll be worth it for you, of course.
For information on these Railcards, and other discounts, try the National Rail discounts page.
EDIT - RAIL PASSES
I'm an idiot, totally forgot about the BritRail Pass. Rick Stein has a page on this, which basically means you can get consecutive day passes, or flexipass, which lets you travel, for example, 15 days of travel in a 2 month period. Prices vary depending on how many days, and what class you want to travel in the trains, but have a look at the site for more information.
Upvote:6
British trains are rather expensive, however there are some options.
If you're a European (but not U.K.) citizen you can buy a 3, 4, 6 or 8 days within 1 month Interrail pass. This allows unlimited travel across on any train for the respective number of days within the UK (A 'One Country' pass). These are cheaper if you're 25 or under (from EUR144 to EUR221) as opposed to 26 or older (EUR212 to EUR329).
For some reason the US / rest of the world version of this, the EURail pass, doesn't include the U.K. Instead, EURail pass holders get a 50% discount on BritRail passes. There are two main types of BritRail pass (travel 3, 4, 8 or 15 days in 2 months, or travel 3, 4, 8, 15, 22 days or 1 month consecutively), with added discounts for being 25 or under. Not only this, but there are regional versions, including:
Assuming you get the 'Scotland, England, Wales' pass, the prices I looked up varied from $109 (EURail pass holder, under 26, 3 days consecutive travel) to $675 (non-EURail pass holder, under 26, 1 month consecutive).
If you're going to Paris you also get a Eurostar discount with the BritRail pass.
Alternatively if you want to keep it structured you can get some great prices on from MyTrainTicket and The TrainLine. Tickets are cheaper the further you book ahead, and also when you avoid 'peak' time (usually before 9:15am).
Finally, never buy tickets at the station. You will almost always pay an absolutely exorbitant amount.
Happy travels!