You should challenge every offence notice an officer gives you. I am not saying that always means pleading not guilty and going to trial, but at least try to minimize the damage to yourself
Can you win? Yes it is possible if you craft a proper defence. I would avoid fighting a case like this yourself, because if you testify, a prosecutor while cross examining you, may be able to find significant weaknesses in your case. Also some people find it challenging to cross-examine a experienced police officer. A trained agent would be able to attend, and you may not be required to attend at all. If your not in court, it is more difficult for the prosecutor to prove your identity.
To prove your innocence in this type of case, based on you message, you may want to establish that the pedestrians and sweeper were a greater distance away than what the officer may have been able to judge. You or your agent would want to obtain the disclosure package to find out what the officer is say about distance, if anything.
You should try to write everything down that you can remember, such as what you said to the officer, what the officer said to you. Did the people you supposedly cut off stop and provide a witness statement to the officer? A worker using a street cleaning machine on a street should be simple to track down. Does he/she feel you cut them off?
What ever you do, do not just pay the fine on the face of the ticket. Talk to agent about it. Most offer a free consultation and they could provide you options that you may not have known about.