Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
Simon Burns
Despite his conservative views, Burns is a "proud" supporter of the more liberal-leaning U.S. Democratic Party. Citing the big tent nature of American political parties, he argues "You can't just say that, because you’re a British Conservative, so you have to be a [U.S.] Republican. American politics isn’t contained in that way. Turn the clock back to the 1970s, and the Democrat Party went from the liberal Kennedy wing right through to the out-and-out racists in the Southern states. The Republican Party had its liberal wing – people like John Lindsay, Chuck Percy and Nelson Rockefeller."