I am logging this issue and solution (below) as, for the second time, I find myself wasting hours on it.
Solution: File -> Settings -> Enter 'Android' into search bar. Select 'Android SDK'.
Select 'edit'. Intellij now asks to download the SDK (~800MB). Intellij becomes unresponsive whilst software downloads and installs (it seems clicking cancel waits until software has downloaded, to cancel). Takes about 5 minutes.