I used to run a railway station and my first suggestion here is that you should NEVER use websites such as TheTrainLine.com. Such sites can't find fares lower than you can get elsewhere and they frequently add on handling charges as well. (Further, I saw plenty of tickets issued by such websites which weren't even valid for travel at all!).
Other than as below, ALL available rail fares are on the National Rail website:
http://nationalrail.co.uk/
The cheapest fares are usually for 'Advance' tickets, which are only ever sold as singles. (There's no such thing as an Advance Return ticket, you have to buy two Advance Singles). However Advance tickets aren't sold on all routes, and they're limited to off-peak services. To get the best deals you often need to book around 5 weeks ahead but some less popular services have Advance tickets available up until the day before travel. The best times to travel are usually between 10am and 3pm on weekdays (or late at night), with Tuesday, Wednesday and Thursday often offering the cheapest fares. At weekends some rail operators offer cheaper 'walk up' fares (e.g. Super Off-Peak Day Returns) than during the week. There are also usually more Advance tickets on offer but they tend to sell out quickly on routes to and from London.
Several rail operators offer '4 for 2' discounts on off-peak services, on certain routes, where 3 or 4 people can travel for the price of 2 (with up to 4 accompanying children travelling for just £1 each, single or return). The National Rail website should automatically offer you those fares if you tell it the size of your party.
The ONLY fares which don't always appear on the National Rail website are those offered by Stageccoach under its Megatrain banner. They're ONLY available on these routes
http://en.wikipedia.org/wiki/Megatrain#Routes
so there's no point looking at the Megatrain website if you're not using one of them. However the website is here:
http://uk.megabus.com/megatrain.aspx
Lastly, remember that railcards can provide extra discounts. If you're travelling with children, a Family & Friends Railcard can help:
http://www.familyandfriends-railcard.co.uk/
If you're over 60, consider a Senior Railcard:
http://www.senior-railcard.co.uk/
If you live in the south-eastern quarter of England, a Network Railcard can help:
http://www.railcard.co.uk/network
Chris