The Fabian school was initiated as a counter to the Lenin approach towards sudden, violent overthrow. The Fabians focused on working through the various core institutions over a period of decades/generations to effectuate a socialist world government.
The problem the Fabians didn't anticipate was that capitalism was so dynamic and produced so much wealth that the targeted proletarians and working class kept getting co-opted by evil private enterprise. That is, they kept receiving raises and ever improving standards of living. Oops, directly counter to what Marx predicted.
So, since the communists couldn't get any of the native populations to readily adopt socialism, the Frankfurt school devised a better method to sow social discord and dissatisfaction by advancing policies aimed at importing poor 3rd world citizens into advanced developed economies.
And here we are ...
Well the Fabians go back to the 1880s, so they were not exactly “initiated” as a counter to Lenin and Bolshevism. But the rivalries within the Left between “reform” and “revolution” aka gradualism vs. violent overthrow exist throughout the past 2 centuries.