It would be helpful if you said what your subject area is. I applied for funding from AHRC (I was a history PhD student) during my first year, and won it for my second year onwards. But I'm not sure if they allow such funding applications any more, in particular they seem, like other UK research councils, to have restricted their funding to certain institutions.
Other options are charity-based funding. I once saw a very useful list of links, but can't find it again now. Maybe Google would help. Again subject is important for this, with charities tending to fund things in specific areas.
Oh and I was a part-time PhD student too.
Good luck!