It is normally called a council house (not a corporation house), and is, as you say, a form of subsidised, municpally provided rented accommodation.
'Corporation' is virtually redundant now as a term for a local council. You used to hear 'the Corpy' in Liverpool, but as far as I am aware, it survives only amongst people who grew up in the 1970s or before.
It does to me too, but there is a play called 'Our Day Out' by Willy Russell, written and set in the 1970s in Liverpool, which contains that usage. It is possible the playwright was behind the times with it, too.