If you do get a wheeled suitcase – make sure it is small. When I was in Spain, an American high school group came on the train with these massive bags and left them in the alley – nobody could move anywhere. It was a nuissance! (and quite embarressing as a fellow American)

The other pitfall of wheeled bags is that many cities in Europe have cobbled streets or steps. The wheels could break off. However, i dont think you will have this problem in the UK.

I absolutely recommend a backpack but its your choice.

In any case, yes, you can leave your bags in the hostel. Some hostels have lockers. For those that dont, do bring a good lock for your luggage.