Can you be a left wing conservative?

The world is run by left-wing conservatives; the progressive-left.

I basically subscribe to a lot of the anarchist, Marxist, socialist etc view of what is wrong with human society and the economic/political order. I just don't know how it could be changed and I am reluctant to get behind any grand plan to change it or even know what I would like the end point to look like. Just need to look at history to see how wrong that can go.

Here are some conservative quotes.

"The political leader knows in advance that all change, however well intentioned, will disrupt the social fabric, with unforeseeable and potentially serious negative consequences. Still more is this true of sweeping, radical change…For radical change to be genuinely worthwhile, it must bring overwhelming social benefit, or be the product of the most extreme necessity. "

"Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. "

I think there is a lot of sense in the above quote and I think that in order for things to change properly it needs to change from below in how people behave and act. I think the role top down management is to poke the "below" to steer it in a direction you would like and react to unintended consequences of the development in where we would like society to be steered.

Am I a left wing conservative? Is that even possible? I think I agree with conservatives on the dangers of fast change or humans attempting to consciously control human societies/economics. However I disagree with what is acceptable to just let happen and I am not at all happy with how things are at the moment. I also think most self described conservatives let a lot of injustices just slide that are unacceptable for me. They are also not very conservative imo, they often want radical change but in another direction. Take the EU as an example. Many conservatives wanted us to leave but I the above conservative quote leads to the conclusion that we should have stayed in the EU. Or conservatives who do not like LGBT rights and the growing tolerance of such people and want to somehow enforce a reverting of the clock.

Christopher Hitchins described himself as a conservative Marxist. Is he an example of a left wing conservative?