I'd treat the two-thirds figure with a hefty pinch of salt. Students are bombarded by e-mails constantly which ask them to participate in umpteen surveys, and the overwhelming majority of students do not get involved with student politics - and are in fact alienated by it. If you don't believe me, check the turnout numbers for elections to your nearest student union - 5% is astonishingly high and practically unheard of. And the people who tend to run (and vote) tend to be an incestuous clique who all know each other.
The image of "Marxist professors indoctrinating students" is something of a panto cliché. More often than not, the kinds of silly policies Johnson is talking about are usually instigated by student unions (see above) or by lazy administrators who want some shorthand way of showing that they are "in touch" with students in the hope that it will affect satisfaction rankings and net the university money.
The Office for Students is a good idea in principle, but the biggest problem with universities is not free speech. The biggest problem with modern universities is that they are expected to deal with tens of thousands of students, and they are expected to act like businesses rather than educational institutions.
This means that you get hundreds of thousands of students going to university because their parents, teachers and mentors tell them that they need to, pay through the nose and accrue enormous debt for the privilege, and in return get courses that are seriously lacking in content, operating at an absolute minimum of cost, and only really teach how to pass a given assessment rather than actual knowledge or skills. This is disgraceful and exploitative behaviour by universities at the expense of people they are supposed to be teaching, who (through no fault of their own) are usually not equipped to realise what is happening to them before it is too late.
So, not a bad idea. But the "free speech" issue is something of a red herring for the real problem of commercialisation, the cult of "customer satisfaction" over education, and profiteering behaviour by universities.