I don’t know if the performance problems are due to lack of skills, lack of interest, competing priorities or whatever…however, here’s some general advice.
The best way to manage team performance is by making the onbjectives clearly visible, the tasks to achieve the objectives visible, the task assignments visible, and the progress against the targets visible. To support this, you need to talk to the people doing the work, and possibly their line managers to make sure they support your project. To protect yourself, and demonstrate due process, I’d have minuted meetings where people make commitments, or you lay down the requirements and the date when it needs to be done, and track the things through….
Then, once you have a documented track record, you have a basis for escalation, and the people will have to do their jobs. It still won’t necessarily get your project delivered though. You need to have a persuasive personality to make people want to achieve for you…that’s not something that you can do with everybody that you meet…
I’d try talking to the team, and explain that this is what you are going to do, so that they understand that you are being fair and reasonable.
Don’t forget to reward good performance. Also, if you can inject some fun into the proceedings (a budget for this is a cheap investment), that can help. It comes down to hearts and minds. If you win them, you’re half way there at the start.