The era when capitalism was considered a radical idea, precedes considerably the conventional categorisation of politics into "left" and "right".
Even today, categorising politics into "left" and "right" is not an exact science. The words often have only a contextual meaning, not an absolute political definition.
The left has typically been associated with radicalism, but these days it's more often associated with "bring back"-style politics. Bring back full employment, social security, universal healthcare, decent housing, rent controls, and so on. Not a very radical realm, really.
Meanwhile, the so-called radical right who promote free markets, have introduced policies that have eroded the economic power and worker skills of Western nations and even crashed the birth rate itself - radical by any view, but neither these radicals nor their opponents are willing to deem their politics "left-wing", since it so clearly assaults the interests of the settled masses.
And there are many other political questions on which nobody seems to agree which wing they belong to.
The confused nature of these categories, then, renders hopeless any attempt to apply them to the past, since it is hopeless to apply them even to the present in an abstract way (i.e. in a way not steeped in our tacit understanding of our own current political context).
Also, back when Parliament was duking it out with Charles I for example - largely regarded as one of the earlier battles of the "old regime" versus capitalist reform - only the rich were represented on either side.
The political interests of the masses in that era were often expressed only through riot and violence, or the implied threat of it, with very little necessarily discussed or committed to the written word, so that the conflict between Charles I and Parliament should largely be seen as a fissure on the right of politics - a fissure amongst competing powerful classes - without significant representation of the masses on one side or the other.