Both times, it was for much the same reason. British politics occasionally seems to slip into a consensus, a status quo bias, that is wrong, and harmful, and needs to be overturned.
Thatcher overturned a political consensus that the mission of the British government was the orderly management of British decline and championed the market capitalism that was needed to make Britain prosperous. Now that market capitalism has deformed into neofeudalism, the political consensus that we need more austerity, fewer public services, lower taxes, no public housing and a collective surrender to the decisions of a handful of corporations needs to be overturned instead.
So I support Jeremy Corbyn for what I consider the obvious reasons.