I was a part-time student, and funded, but AHRC is AFAIK a bit unusual in funding people part-time. I also got a stipend in the last 18 months of my funding, cos they'd changed the rules so part-timers were on more of an even footing with full-timers.
Also my award was direct to me, rather than through a university. That's not normal with other funding councils.
Have you asked your likely supervisor for advice? There are also charitable trusts who can fund people. For example in Scotland we have the Carnegie Trust. Maybe there's something similar for Wales? But then again they tend to fund full-time only too.