I got a part time job last year without too much difficulty. It's worth asking friends with jobs if their work is needing new people. If you've got experience with bar work, then there's often work for things like the Christmas Ball, which could be good as a one-off.
I don't see people here fighting each other too much for part-time jobs, to be honest. I think if you genuinely wanted and needed to work, then you'd almost certainly manage to find something. It might be worth your while sending your CVs to businesses before you get here, I don't know.