Joćo,
If you can travel light, do so. Public transport in the UK (as it is in many countries) is hard to get around on if you have a lot of luggage. Are you bringing a bouldering mat with you? If so, you'll be best to get the train from London to Sheffield. For booking tickets for the train, thetrainline.com allows you to do this online and receive your tickets in advance if you wish.
If you don't have a bouldering mat, you can often find cheap one way bus tickets which allow a relatively small amount of passenger luggage (large rucksack and a small one as hand luggage).
The biggest coach transport provider is the National Express. If you check
this link out, you'll be able to see the booking form for getting cheap single tickets. If you know in advance when you're going to be returning to London, you could maybe book another single? Either way, the National Express site will allow you to look at coach fares, times and routes.
You won't be stuck for people to climb with in Sheffield. That's a guarantee.
(Exactly what Houdini said
)
