Recently in the month of July my Mum & her sister who lives half a mile away both had a large influx of rather docile flies. A pest control man said they were rain-flies & would be gone in a couple of ...
Your pest control guy was correct.
Rain-flies are very short-lived flies that come to life during the rains. They complete their life cycle under the ground and come up through small holes on the ground. Every colony will thus be home to hundreds of them.
Though they can be seen during the day, mostly they come out into the open at night in their first outing as fully grown flies. They are attracted by light and can thus actually create a lot of nuisance inside homes.
In our village in India, where I grew up, we used to make bonfires, which attracted these flies, as the only way to deal with their 'menace'. Our cats used to snack on them - a literally endless supply of them !
As you have rightly said, they are very docile, harmless beings. They normally do not live beyond 24 hours after their metamorphosis into adult flies.
Here is a pic of those humble creatures.