I studied for my phd part-time while working fulltime/having children. I had an idea of an under-researched area with two consultants where I worked. The consultants had both been phd supervisors previously so were happy to support me to approach a uni. I produced a 'titled' document with a small literature review highlighting the area of research, worked out the experimental design to facilitate the research, costs incurred with evidence of funding/finances and then gave an estimated timeframe for the work/write-up to be done. I also produced a supporting cv of my quals, prev work/research experience, publications and supporting evidence for my application. I contacted the uni in Cambridge with my propsal and after consideration it was accepted. They also provided a 'uni' supervisor for my studies who was principally there to guide me through the paperwork required and uni standards, although he did also have a strong interest/knowledge in my research area and did a fab job!