This guy is clearly flying with one hand on the yoke..
However RAF pilots were advised to use 2 hands when firing, to brace, mainly.
I've read one account where the pilot of a Spitfire put both feet on the instrument panel and 2 hands on the stick to get out of a dive... That would be a cool animation.. Desperation mode!
I think the basic answer is they used 2 hands only if they needed to. I don't think you'd abandon the throttle in combat unless you had to. (I can't think why, all spitfire pilots say that you only had to twitch your hand and the aircraft twitched too, a very responsive aircraft).
The only time Spitfires stiffened up was at very high speed.
Fact is you'd pass out from the G before you ever needed 2 hands because a Spitfire got 'heavy'.
I've got 100's of RAF pilots BoB accounts and there is reference to throttle adjustments, turning the sights on, adjusting the sights etc, all during combat. The only time I see any reference to stiff controls is when the Aircraft was up near 400mph.