I recently bought a TV/monitor and I don't have a licence. I also live in a converted Victorian house and each flat has to have a licence.
The TV Licensing people wrote to me a few weeks later asking why I didn't have a licence and I told them it was for my PC and not for watching TV. They told me that was fine as long as I didn't watch stuff online as it was broadcast. I do watch a lot of stuff on iPlayer and such but I just check to make sure that it isn't being broadcast when I want to watch.
The TV Licensing people wrote to me a few weeks later asking why I didn't have a licence and I told them it was for my PC and not for watching TV. They told me that was fine as long as I didn't watch stuff online as it was broadcast. I do watch a lot of stuff on iPlayer and such but I just check to make sure that it isn't being broadcast when I want to watch.