Again, I wonder how the self-defence argument would go in this scenario; if some random person in the street jumped on me and pinned me to the floor for no reason* then I certainly wouldn't just lie there passively and let them do whatever they wanted with me!
* e.g. in the case of mistaken identity, there would be "no reason" as far as I was aware
There's a key requirement within that legislation:
"A person other than a constable may arrest without a warrant—
(a)anyone who is in the act of committing an indictable offence;
(b)anyone whom he has reasonable grounds for suspecting to be committing an indictable offence."
Assuming the OP's story is true, then this incident occurred purely on the word of a random stranger at their table saying something to the bouncer.
I certainly wouldn't want to be the person trying to justify that to a judge as "reasonable grounds"!