The National Theatre has announced a free to watch at home weekly programme starting 2 April 2020 and following every Thursday.
Follow the link here to find the productions previously screened in cinemas globally as a part of National Theatre Live and which will now be available online. The first production will be One Man Two Guvnors featuring a performance from James Corden. Each production will be free and screened live every Thursday at 7:00pm; it will then be available on demand for seven days.
Also,students in UK state-funded schools can access the NY collection of 20 productions for free see here.
OutIn has a regularly updated list of theatre productions available to view online.
Andrew Lloyd Webber is streaming his musicals online in the series: "The Shows Must Go On" here: YouTube channel.
Southwark Playhouse (or Southwark Stayhouse!) are streaming productions here.