Given that other close-contact industries are reopening on 04 July (subject to no surge in reinfection rate), I think it's safe to state that PPL flight training will be allowed to recommence at the same time, but it may be in England only for the time being if the devolved nations aren't willing to follow suit yet.
Concerning facemasks, some ATOs are using them and some aren't. Heat is one factor that has deterred some from wearing them, and I've also heard the CO2 retention argument. As there is no way a school can 100% guarantee a coronavirus-free zone, I think the decision should be left to those sharing the cockpit.
Is anyone going to brave the trial lesson market in the near future? As a significant cash cow for the grass roots training industry, I can imagine that commercial pressure will play a part in this, but will it prove a step too far for instructors?