There are a number of suggestions I can make, but the problem is if you use London Midland from Crewe for example, and are just going for the day, by the time you've got there it's time to come back! The only real option in this case is the Virgin train from Preston - around 2h15 from Preston to London Euston.
Firstly, Virgin West Coast priced fares never seem to enjoy any good splitting possibilities. :-x
For advance fares the key is to book as early as possible (as usual) - to get the very cheapest deals book as soon as they are released.
Check the calender here.. I've found weekends are probably cheapest for a day trip. The
very cheapest for 3 with 1 railcard is £77.10 return - that's two Advance singles from Kirkham and Wesham to London Euston.
It's a long shot but if anyone collects Tesco clubcard points you can exchange the vouchers for tickets on
RedSpottedHanky you can get three times the vouchers value in rail tickets. So you'd need around £25 to buy the cheapest ticket.
If you really want to save money - Megabus have some good deals in summer (TIP: book one seat at a time to get it cheaper). You get something like 10% off with an NUS Extra card. Return for 3 from Preston to London can be had for about £24 if you look carefully. But again around 12 hours on a coach in a day is pretty rubbish.