How to generate route to pass through polygons?

Question

A twist on a standard problem. I'm looking to plot a route through all the wards in London (649). I have all the wards as a shapefile and ideally i wanted to let the computer generate a spiral route staring at the outer edge of london working inward to the centre. My thoughts of how to approach;

1. Assign each polygon a centroid.
2. Generate route to pass though points, outputting a line
3. Create a buffer round that line (to select all nearby minor roads)
4. Generate final route by rerunning algorithm along the roads

Does that approach seem valid with the tool sets available?

Image of polygons as below