Please put aside whose video this is, and who was asking the questions, and the crude editing of parts of the video (which may have made the BBC reporter sound more defensive than he actually was and which leaves open the troubling questions, 'Is this what he said in full?' and 'Is he being fairly presented?') and just focus on what the BBC reporter said in answer to the questions put to him (especially in the unedited later bit of the video):
YouTube interviewer: When you describe this crowd, how are you going to describe them in your news report?
BBC reporter: Er, well, we're going to call them...well, you've called...you've labelled yourself as an 'anti-extremist movement'...
YouTube interviewer: When your news report comes out on this will you mention the word 'far-right'?
BBC reporter: If people label it as such then we have to reflect that, yes.
YouTube interviewer: No, you should report and reflect what you've met and seen today. Have you seen far-right demonstrators?
BBC reporter: If people label it as such...
YouTube interviewer: If I label you as 'a nonce' would you report that you're a nonce? What you do is word-association - which is what all the media do against ordinary people. These are ordinary people who have come out to demonstrate. You will do word-association of 'racism' and 'far-right'. You've got ordinary people who are demonstrating against terrorism and you...every time the mainstream media...you brand them, and it's not fair. It's not right. And you know that because you're on this demonstration.
BBC reporter: I'm sure you know where those labels come from. You have calls for tighter immigration. That is a right-wing rhetoric.
YouTube interviewer: So calls for tighter immigration against Islamic terrorism is 'a right-wing rhetoric'? In fact the Labour Party talk about controls on immigration. Everyone does. What do you mean 'a right-wing rhetoric'? How it that 'right-wing rhetoric'?
BBC reporter: Well, but people would say that. That is by...
YouTube interviewer: So because this group talks about terrorism and talks about controlling borders that means they're 'far-right'?
BBC reporter: It's a far-right...yeah, they could be.
YouTube interviewer: This is what you're up against! This is what you're up against! This is the BBC. So if someone identifies as wanting to stop Islamic terrorism and controlling your borders it's 'far-right'.
BBC reporter: It would be labelled as such...
YouTube interviewer: By people like you!
BBC reporter: But my opinion is absolutely invalid. It's about getting...
YouTube interviewer: But you're reporting for the BBC. You're lying for the BBC. You are officially fake news. You are demonising so many innocent people...
BBC reporter: Right.
YouTube interviewer: You make it impossible for people to talk. And that's who you are. You're here to try and get bad footage. That's why you're here.
BBC reporter: Right.
YouTube interviewer: That's your agenda...
BBC reporter: You're frustrated with the media, from what I take from this?
YouTube interviewer: You have a complete agenda when you come to these demonstrations. And you don't usually report it. If you don't get any bad footage of today, if you can't get violence, you don't report.
BBC reporter: Do you think there will be violence today? I mean, it's been peaceful so far.
YouTube interviewer: No. Not unless far-left demonstrators are allowed to get up and throw things at people, which is what usually happens. So if the people want to stitch people up, which we see time and time again, then we'll see. But you are all part of the problem.
Isn't that revealing? The BBC reporter (or producer) is maintaining his - and the BBC's - impartiality but says that this protest by the Football Lads Alliance will be labelled as 'far-right' by the BBC because (unspecified) people label it as such.
He also openly states his own opinion that calling for tighter immigration is "a right-wing rhetoric" - a particularly revealing insight into BBC groupthink.
And when the YouTube interviewer states that the BBC's agenda will dictate that it won't report the protest unless there's "bad footage", the BBC reporter asks if the YouTube interviewer thinks there will be violence today....and, yes, the YouTube interviewer was correct in his prediction that because there was no 'bad footage', no violence, the BBC wouldn't report this demonstration, and they didn't.
I don't know who the BBC reporter/producer was. The YouTube interviewer, however, was Tommy Robinson.