Plan out your travels wisely. Map out where and what you want to see and be realistic about what you can do with the time and money you have. This will give you a clear idea of what and how to do it.
Purchasing train tickets weeks beforehand is a good idea and look into the possible deals you can get if you are affiliated to certain airlines and other businesses. It is best to purchase the tickets either online or on a personal basis (where sometimes you can get better, more personalized deals). When you are booking via train expect to know that you might have to travel a couple more hours but it is much likelier that you will reduce the costs by half by doing this.
Another very cheap way to travel is through Megabus. Megabus is a bus company that offers very cheap fares for travel to England, Ireland and Scotland and the surrounding areas. The buses are quite comfortable and can range from 6 to 20 pounds round trip. The key to purchasing these tickets is purchasing them online, and it is necessary to have a printed copy of your ticket.
When you purchase tickets for underground and bus your best bet is to purchase an oyster card or bus cards. These give you unlimited travel for a week and end up being much cheaper in the end.
When traveling you can also stay in cheaper hostels as opposed to expensive hotels, which can also diminish the costs of travels increasingly.