if a police officer puts their hands on you
Sorry mate, as soon as you get behind the wheel of a car, you are operating under a whole new set of rules, laws and
In the UK, if a police officer puts their hands on you without your consent and with no probable cause, are you legally allowed to act in self defence?

I have been a police officer and during training was warned about this specific scenario. So officers in the UK are allowed to use force in one of 3 common situations, 1. Self defence or defence of others 2, to make a lawful arrest or 3, to keep the peace. So if an officer decides to start shoving someone about for no reason (theoretically) and that person defended themselves then yes it would be legal. We were told this by the instructor.
But the flip side of this is that the police tend to know certain bits of the law really really well. The fact that in the example put as a comment on another answer, that you might feel there is no grounds for you to be arrested or detained in no way means that this actually is the case in law You don't know what intelligence the police officer in question has that he is working on and if you think you are using self defence you will just make things worse and I 100%guarentee you won't change the outcome. Police in the UK are almost never alone and officers are close by so you will just get hurt. Police really aren't in the business of wasting their own time and making pointless arrests, it looks bad on them and takes up a lot of time. I always advise people to cooperate with the police and never escalate a situation.
I had a situation many many years ago when I was asked to leave a club because I had had too much to drink but causing no trouble, but the bouncers didn't let me pick up my jacket first and it had all my stuff in it. They wouldn't let me in to get it so I approched some officers. I was clearly very drunk and angry and one of them did put his hands on my arm and say calm down. Now he is putting hands on me and none of the above three criteria are filled, by the letter of the rules I could have pushed him away at which point I would have been arrested for being drunk and disorderly, spent the night in the cells and probably not got my stuff back for a while.
As it was I did calm down, explained the problem and they went and spoke to the bouncers who agreed to let me back in to get my stuff, nothing escalated, no problems.
Many see the police as useless. Many as effiecient at doing their jobs, but, sadly, when you look at the statistics and how many crimes go without being solved - and how many are not even looked at because of shortage of manpower, finances and time - it seems that the police are over worked and too few to cope.
taking them off the streets and relying on cameras alone is a BIG mistake as they have lost all faith from the people, - the people they look after and not the people they think they have to police.
I am NOT policed by the police - they work for me - they are paid to protect and serve and that means me, and you and every breathing person in this country and maybe some day they will realise that we are not all criminals, not all out to break the law, not all ignorant and not all from a broken home and if we are, is not a reason to assume anything until proven guilty.
