If they're considering charges under the Malicious Communications Act 1988, then they'll have to prove, among other things, his state of mind when he published the leaflets -- in particular, that his intent was "to cause distress or anxiety" to its recipients ("malicious" -- meaning that he actually intended to cause these emotions in the document's intended or likely readers -- in this case, anyone who might reasonably be expected to see it online, I guess). It's an either-way offence, punishable by 6 months in the Magistrates' Court or 2 years in a Crown Court.
There's a weird grey area in English communications law, which hasn't really ever properly caught up with answering machines and faxes, let alone the internet and social media, so it tends to treat messages posted online as being addressed to personally to anyone who might see them (so the entire readership of Twitter or Facebook), in the same way it would treat a letter, email or phone call.
If you recall, there were several contentious prosecutions a few years ago (several while Keir Starmer was DPP, as it happens) which brought some clarity to what's lawful and what's not -- remembe
r the Robin Hood Airport twitter bomb threat case? -- which sought to clarify the matter, which they did to some degree, and while there may be a Malicious Communications Act offence to answer, depending on the exact words complained about (though I doubt they could proved intent to the necessary standard), I wouldn't give much for its chances if a prosecution ever materialises.
Since I've not seen the leaflet in question and don't know the facts surrounding its publication, apart from what I've read here, obviously I don't know what there is for the prosecutor to consider, but she or he will doubtless have in mind para 34 and following of
this CPS guidance (still in force, AFAIK) when considering the file and whether to prosecute:
In these circumstances there is the potential for a chilling effect on free speech and prosecutors should exercise considerable caution before bringing charges under section 1 of the Malicious Communications Act 1988 and section 127 of the Communications Act 2003. There is a high threshold that must be met before the evidential stage in the Code for Crown Prosecutors will be met. Furthermore, even if the high evidential threshold is met, in many cases a prosecution is unlikely to be required in the public interest.
ETA: The more I think about it, the larger seems the legal can of worms this prosecution would open. I'd be very surprised if the CPS want to pursue it, because of the Human Rights Act implications.