Yesterday at 11:30
I think David is right. You need to spray at the first sign of mildew and keep at it, or it will creep up on you... Mildews are specific to the host plant so rose mildew won't spread to other plants. And some cultivars are more susceptible than others, which might explain why only one of your roses is affected, Tom McF.
Water stress seems to be the main reason plants are affected with mildew, which is why climbing roses on walls often get it badly. Regularity of watering is very important, and mulching to keep the moisture in can help too. The fungus spreads most rapidly when the temperature is in the low 20s, which just about covers the average British summer... The spores over-winter on leaf litter so clearing up and burning or binning fallen leaves around the infected plants is a must.
Ginger, hard luck with the begonias! It's really difficult to keep hanging baskets sufficiently moist when it's a dry summer, even if you water every day - and the air circulation is often not very good, because you want your plants packed closely together to give a good display. You could try an organic spray (I think there's one made by Vitax) if you don't fancy chemicals, though it might be too late to make them look good this year