Despite what they may say, universities really do have money to burn. I'm sure if you gave them a call they would be able to sort you out with expenses, but if not:
Book well in advance. Compared to booking tickets on the day, booking a month or two in advance can cut the price in half (or more).
Buy a railcard. It saves a third off your rail fares and only costs £28.
Buy rail tickets in person. Because of the complicated ticket system, sometimes the operator can pull a trick that saves you money. Yesterday I had to take the train to Newcastle and hadn't booked my tickets in advance. The national rail website told me a return would be £108 but by booking tickets for a station past Newcastle, the operator got me a return for £57. I have no idea how this worked.
Travel by coach. Like others have said, Megabus is amazing for cheap travel.