I think you have three choices, all of which are acceptable and defendable paths to take.
1-Stay where you are and try to improve the situation for yourself and the team. Can you find new work or clients and support the management? If you can do this, it would be a great achievement and should attract recognition from your employer.
2-Move to another part of the organisation. It may be that you have skills that are in demand elsewhere in the 'large consultancy'-Project Management or Stakeholder Management, for example.
3-Leave. But be honest with yourself and future employers. Why are you going? Is it because of the lack of work, or that consulting's not for you or you don't like the firm? Think this through and once you've decided to go, go!
The worst thing would be to stay just for the benefit of you CV - you're not going to produce goo results if you're just killing time before you can leave. I've done it for a period and watch others doing it too. To managers, it's very obvious if your heart's not in to what you're doing. Good luck!