It was certainly a controversial appointment because he was succeeding Laski.  There is some discussion of hostile reaction to his appointment by Crossman, in Paul Franco's Michael Oakeshott: An Introduction, p. 13.

I'm not sure where to go for what stands behind the appointment, other than suggesting that you might try the L.S.E. archives; there are, though, quite a few people who have worked on Oakeshott and you might try them individually.

One interesting earlier reaction to Oakshott, is on the second page of Popper's 'Towards a Rational Theory of Tradition' in his Conjectures and REfutations (the original version of the paper having been published in 1949.

Jeremy Shearmur
________________________________________
From: Societies for the History of Economics <[log in to unmask]> on behalf of Rob Tye <[log in to unmask]>
Sent: Thursday, 14 August 2014 6:13 PM
To: [log in to unmask]
Subject: [SHOE] Oakeshott

A few people have suggested Oakeshott's 1951 appointment at LSE was viewed
as controversial at the time, but I have not been able to find any names
mentioned as canvassing in his favour.  Can anyone throw light on this?
   The promised biography by Robert Grant ought to assist, does anyone know
when, or if, this is now expected?

Rob Tye