There are varieties of runners that have white flowers. In the 2nd photo it looks as if the beans are starting to go to seed... when did you plant them and where do you live in the UK?

It would be better to pick them well before the beans grow fat, unless you are growing them to dry the beans for later.
The pods normally get stringier as they mature. unless you are growing a stringless variety.

These are a bit like the ones you get in the supermarkets, flat with wavy edges showing the beans. I think they are called 'pole beans'.

I'm thinking that they are an Italian variety of snap bean, left on the vine too long.