Pollination tends to be a highly localized event. So a runner bean is most likely to be self-pollinated, then somewhat likely to be pollinated by it's closest neighbors, and then a slight chance of being pollinated by something from further away.
The best way to insure that a variety stays inbred, is to only plant one variety. But if your neighbors in nearby allotments also plant runner beans, then all bets are off.
It looks like some of the varieties you planted were genetically diverse to start with, so you can't really keep those varieties pure, because you don't have any way of knowing what "pure" is.
You had a couple of varieties with white seeds. Late in the growing season, you will be able to tell if they were pollinated by something with colored seed. By that time, the plants have already been shedding pollen into the patch. You won't be able to tell by looking at the seeds if the white varieties pollinated each other. Perhaps there are differences in the pods, and especially in the flower color. For example, I suspect that plants with white flowers produce white beans. If you have a colored flower among the white bean patch, it could be culled early in the growing season to keep it from releasing pollen into the white patch. Some of my runner beans have bi-colored flowers, or pink flowers. That might be a clue that a plant is off-type.
You can certainly grow out the seed that you saved, and reselect each year for your preferred phenotypes. If you want only white seeds, then only replant white seeds.
To complicate matters even more, runner bean pollen can sometimes pollinate common beans...
My preference is to grow every crop as a landrace. So I'm thrilled whenever I can identify a naturally occurring hybrid. I don't even mind if my landraces have multiple species in them.
Bi-color runner bean flower:
I grow my runner beans all jumbled together:
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