I disagree that it's not in the public interest to prosecute someone who may have pushed a cyclist into a canal.
It is not in the public interest if there is no real supporting evidence
assuming the 3rd party doesn;t want to be involved - as opposed to actively supporter her partner's statement
then all the evidence is that there was a heated discussion
then she started off again and fell into the water
what cause it is not clear
she says he pushed her
he says her handlebar hit him and she fell in
she might have just lost control on a bumpy path edge
any could be true
personally I think she is telling the truth - or something close to it
but I cant prove it beyond reasonable doubt
and you can;t charge someone without evidence that their story is true
basically - if I was passing someone on a canal and they fell in
I would be very annoyed if they then got me arrested just on their says so that I pushed them - no matter what was said