HR at work have been useless so I'll turn to RAWK for expert advice,
There's a lot of considerations and unknowns for us to give you thorough advice mate and please note I'm not a HR expert, just a senior manager.
Assuming its quite a large organisation because you have a HR dept. Despite you not getting sufficient advice from HR you still need to adhere to company policy, find out where your Performance Policy is and get fully familiar with it. It sounds like you've already had informal 1-1 chats so the soft management route (which I always recommend) has been exhausted. It sounds like you need to meet with her and her TU rep (if applicable). Again depending on Policy you still might want to make this informal, an honest chat without inviting her in writing to attend.
Before I make the next point you'll have to consider your own position in the company, what status do you have, can you impose an action plan without her ignoring it or the TU undermining it. If so then be completely honest and gently ruthless and tell her you'll need to micro-manage her if there isn't a tangible improvement within 2-weeks which must continue or you'll invoke the disciplinary procedure.
You'll need to set targets and expectations without singling her out, you may need to apply them across the team but still tell her its her that being monitored.
You can discuss with her whether the structure she works under is fit-for-purpose and that you'll introduce a review if the team isn't performing overall and that may impact her (although team reviews are not the best way to manage performance - you should be tackling it).
You need to make sure she is unequivocally aware that she has placed a spotlight on herself and you have a duty of care to the other staff to manage the situation.
If she fails, again, you'll need to know the disciplinary policy as you may need to step back from that and someone neutral takes over an investigation.
Record everything if you don't already - from today, not Monday, write everything down.
I'd advise anyone going in to management who suspects they have a poor worker to keep a diary of that person from day 1. Even if you can never use all of the information formally because it looks like you're case building it serves as a reminder and you can at least contradict an employee if they ever deny doing anything months after an incident - we all forget stuff.
I empathise mate, I had a very long, overdue and ruthless chat with one of my team last Friday morning. At first he threatened to leave the meeting and I told him if he is not receptive to my ideas we've got a bigger problem than I thought and he is going to make himself very vulnerable as an employee.
Happy to help via pm if you want but as I say I'm just an experienced manager not a HR expert.
typos edited