I travelled around because I had saved a little money from my job during my gap year, and I quit my job in June, three months before uni began. Which left me free reign to travel for three months! Which I didn't do because I spent obscene amounts of money on my ex but oh well, I was still able to make some nice holidays and by being clever, I made my money go far. A few examples include:
-I mostly stayed in hostels, which aren't ideal but they are so much cheaper than hotels
-I pre-booked stuff as much in advance as possible
-I was flexible with my travels so I could choose the cheapest options - for example, the exact days I went to France were determined by the days in which the Eurostar was cheapest. Also, the time of day affects prices a lot - if you travel in the early mornings, prices tend to be cheaper.
-I got myself a 16-25 railcard, which is just the gift that keeps on giving. I'm of the opinion that trains are the superior form of travel so I travel by them whenever I can. I guesstimate the 16-25 railcard has saved me something like £500 in just a year and a bit I've had it, and it has nearly two years left on it. At £70, it's a steep investment but you sure make a return, and then some more. I get it's more glamorous to go abroad, but the UK is a beautiful place with plenty to do and see. I get that it has an allure to me, as a foreigner here, that British people lack (because that's just how it works in every country), but do try to appreciate some of the things here and put your pretend-to-be-a-foreigner goggles on.
-But also you can travel on cheaper methods of transport, like coaches. Trains are faster, more comfortable and they usually have prettier sights than coaches, but that's a compromise I choose to make but you can do what you want and travel even cheaper around the UK by coaches.
You just hunt around for deals too - like Eurostar offers these really cheap fares at the end of the summer for £39 (last year's prices), or you travel on budget airlines, which aren't the best but I did a round trip to Dublin from London once for the modest price of £60, and split the price of a hotel room with some friends I was sharing with. Also, when I'm travelling, you probably shouldn't do this but I live on a literal croissant and coffee for breakfast and a sandwich for lunch most days I'm away travelling, and maybe some unhealthy snack for dinner. I will only go onto a restaurant and have a nice but expensive meal once every three or four days or so. Probably not the best thing to do but it keeps costs down. Also helps if you're travelling to some place in which a friend or an acquaintance lives so you can crash at their place
I hope this gives you a rough idea of keeping things cheap. But my last tip is, save money! Get your paycheck and automatically stick some money in a savings account and don't touch that. You'll thank yourself later.