Yes, it's going to depend on who funds you and your university policies. I'm funded by my department and I don't have any extra funding for things like research costs or conferences, while people in my department who are part of an EPSRC project have a small fund built into their project for extra research expenses. But I think computers are a bit different - my department gave me a brand new laptop when I started, and I think that was the case for everyone, however they were funded. I'd be extremely surprised if a university didn't have a system in place for providing computer equipment, it's not like you'd be able to do a PhD without one.