And did MI5 really think he was working for the KGB?
I don't know if this is something historians today would actually know, but I'd be interested to hear any answers about sources, evidence, etc.
The answer is no. While MI5 had a file on him, which noted that he had contacts with Communists, Russians and even members of the KGB, MI5 never actively investigated him.
See: Christopher Andrew, The Defence of the Realm: The Authorized History of MI5 (London: Penguin, 2009, 2010), p. 632.