Are your bean flowers getting pollinated? If not they will just drop off and no beans will set. Get a child's paintbrush or a q-tip and pollinate yourself if you don't see any insects around. I hope you have not sprayed with an insecticide as this will deter the friendly insects and kill them too.

Are the white flowering beans climbing French beans rather than runners? If so, these set beans and manage to grow well in dry conditions far more easily than runners.
In my experience runners always start by dropping most of their flowers and it's only later when they have made a lot of growth that they start to produce their bumper crops, usually in cooler conditions of late summer and autumn (or in the UK, that's usually mid-August isn't it?)
It's always explained as lack of moisture or pollination, but it is probably down to both. Bear in mind runner beans, Phaseolus coccineus ssp. coccineus, originate from cool mountain areas in central America where there is heavy rainfall.