If you are ever planning to travel by rail in the UK, there are two invaluable web sites. The first railtrack.co.uk will show you timetables for the entire country; simply enter your starting point, destination and preferred timings and it will come up with the options. You can ask for earlier and later journeys. However, this site does not show prices, so for this you need to go to: thetrainline.com
Here in the UK, if you book your train fare one week, two weeks and further, in advance, you can achieve substantial savings. Even buying a ticket to pick up the next day at the station can make a big difference in price.
The two rail journeys where buying tickets in advance makes no difference is the Heathrow Express, the £12, 15 minute journey from London Paddington railway station to London Heathrow airport, and the Gatwick Express costing £11, and taking 30 minutes from London’s Victoria railway station to Gatwick.