To get anywhere in England its quite expensive. If you want to travel by train it's advisible to book in advance. Check out thetrainline. When you get to the pricing page check out the single tickets. By buying two single tickets you end up getting a much cheaper journey if you're doing a return.
Another option which is the cheapest way of getting to the major cities is via the megabus. There are no stops between cities but that's probably one of the reasons why its so cheap. For example you can get to Leeds from London for £2.50 return, whereas by train its £75 return. If you want the really cheap fares its best to book in advance but even the next day it can be as little as £13.50. You are travelling on refurbished double-decker buses and travelling on motorways so its not the best way to travel but its stupidly cheap!
A lot of people who visit England only seem to go to London but there is sooo much more to see than there, and everywhere else is a hell of a lot cheaper!

Good advice...

The other one that I use a lot is National Express because they do things called "FunFares" which are between major cities for as little as £1 each way...

I haven't travelled on MegaBus but I have heard both good things and bad things about it...good things being that it is cheap and cheerful...and the bad thing is that they occasionally break down, but that can be said for any company...things happen now and again.

However you choose to travel, it's cheapest if you book several weeks in advance. If you make a last-minute decision then usually the bus will be the cheapest way to get around.

If you're 18-25 and planning to spend more than £60 on train tickets, then get yourself a Young Persons Railcard: it costs £20 and saves you 1/3 on nearly all fares for a year. Available to everyone with a passport photo and proof of age. Buy at any staffed station (including airports, I think).