Just good maintenance really, pests like greenfly etc can come in from anywhere as there is a generation of winged ones. encourage birds and other predatory insects in to your garden.

Mildew could be down to the weather at present and yours will be less susceptible to this if they are well watered, fed and given plenty of ventilation. Perhaps the plants they are growing are less resistant to it than the varieties you are growing.

Perhaps they haven't noticed there are any problems and if not you could offer friendly advice re the black spot [remove fallen leaves etc]

You could ask them if they'd like to borrow your black spot spray???

Thanks for your help ladies. Unfortunately I don't really know my neighbour enough to offer help. It might not be well received. I have googled the problem and I'm trying a mouthwash mixture it suggests, so far things are looking much better.