I have not seen many successful independent consultants who did not already have a strong body of professional work prior to hanging out their shingle. You need to have people who will provide references regarding the quality of your work, examples of results you’ve delivered, and maybe even some intellectual capital in the form of panel presentations or articles. However, the experience need not be exactly the same as the consulting value proposition. For example, you may have worked in marketing for brick-and-mortar retailers, but your consulting business may focus on E-tailing. Or you may have worked in real estate, but now focus on green building. The important thing is that there is some link between your experience and your consulting practice.
In terms of building the network, you should take two approaches. Start with people in your existing network, and then grow organically from that community. Then develop a list of 10-12 key organizations you want to know, and proactively build your expertise and relationships into those organizations. Bottoms up and top down simultaneously can be a very effective strategy.