"So pretending a famous leader is still alive while in fact he isn't makes him....real?"
I think that might be quite possible. It could occur if the oligarchs ruling Oceania all lack the clout to seize power for themselves individually and replace the cult centred around Big Brother with one based on their person.
So in order to give their regime legitimacy, they instead choose to continue as if Big Brother was still among the living and propagate a personality cult that makes him appear as a demigod - in North Korea, after all, Kim Il-sung is officially eternal president of the republic, only in this case the party inner circle would even deny that Big Brother had died in the first place.
As for Ken Livingstone, he was born in 1945, so he would still be very young when the revolution occurs. Though that might not prevent him from getting involved in it later on - once he rises to power, he could have history re-written in order for him to appear to have been involved from the start, even though that would not have been possible due to his youth (Kim Il-sung had history re-written so that he appeared to have been the supreme commander of all Korean resistance forces to the Japanese, whereas in fact he was just one of many, similarly to the fact that it is stated that Kim Jong-il was born on Mount Paektu in North Korea, whereas in fact he was born in Russia).
The problem is, of course, that the earliest date at which Livingstone would be able to become very active would be the late 70s (Beria became first party secretary for Georgia at age 32, so it is not wholly implausible for an alternate Livingstone to achieve something similar).
Based on what I know, the concept of Big Brother would by that time already have been set in stone, meaning that there must have been a Big Brother - unless, of course, Livingstone perhaps usurps the role of Big Brother instead of becoming the original one in the first place.