I'm married with a child and consequently not able to move to the universities which have the supervisors I'd really like to work with. How important is it to be based near the university you are doing your research? Is it feasible to apply somewhere, but only visit for fortnightly meetings? Or, how likely is it that I could be based at my local university (where I'm about to start teaching) but have a supervisor from a different university? What are the pros and cons of being some distance away?

I considered a PhD by distance after failing to get funding, resulting in me not being able to afford to live in my chosen university's city. In the end, my supervisor agreed to let me live at home and study by distance unofficially so that I could keep working with her - I however had the advantage that she was my MA supervisor previously, so knew that I have the motivation/stamina to do it while away from campus. It might be more difficult to persuade an academic who doesn't already know you to make that commitment.

It also depends on whether your subject area lends itself to distance learning - if it's an area that requires lab access/specialist equipment or facilities, then you might struggle.

The feasibility of only attending fortnightly will depend on how far away the institution is. I have heard of people having supervisors from more than one university, but that may depend on whether they have worked together in the past and whether both universities have the same facilities/opportunities in your subject area.

I've been 250 miles away from my university throughout my whole PhD. I visit every couple of months and catch up with my supervisor via email. It is hard but do-able.

Yeh, it's perfectly feasible and people do things like this. Some unis might have better facilities to facilitate it , for example video conferencing so that you could also attend seminars and lab group meetings for example and not have to either travel in or miss out. Fortnightly meetings is also totally feasible. I think it's just about finding some opportunities that you think would suit you and making your pitch / proposal.