Looks like a runner bean, Phaseolus coccineus. Red and bi-coloured flowers produce speckled seed but white flowered cultivars can have white beans. The people on the Beans, Peas and Legumes Forum can tell you which varieties grown in your area would have all white beans. The cultivars I grow all have speckled.

I have the white beans from the plant in the picture.
are these beans edible?

In the UK runner beans are widely grown as a vegetable and seldom as an ornamental. They are eaten pretty much exclusively as green beans and never as either shellies or dried beans. However, there is nothing to stop you eating them in those ways. Personally I don't like the beans much. We only ever eat the pods before the beans have matured, or even formed much.

I also think you should repost on the Beans, Peas and Legumes Forum because so far you only have my opinion on what these are. Can you show a picture of the beans (with a scale in the picture). And are there any flowers left you could show?

Here is a link that might be useful: Beans, Peas and Legumes Forum

How do you know they're NOT lima beans?

I've never seen Phaseolus lunatus (Lima beans) so they could well be that.

Maybe Canavalia ensiformis, jack bean.

Here is a link that might be useful: Canavalia ensiformis, jack bean