I am pretty sure this has nothing to do with reporting restrictions.

In the source quoted by Polangmar, a questioner who is to appear in court asks whether the local press can report his name. The legal expert asks him what the offence is (under which section of which act he is charged). The questioner answers that the summons specifies section 4 of the Public Order Act and also quotes "H.O. 125/11 local none CJS PU86004". The lawyer tells him that there are no reporting restrictions for that offence.

It does not follow, however, that the lawyer has deduced this from the words "local none". He didn't enquire about this element; the questioner reported it as additional information. The lawyer clearly deduced the absence of reporting restrictions from the section and act, which is what he asked about. Very few offences indeed carry automatic reporting restrictions that prohibit publication of the defendant's name. By statute it applies mainly to youth courts.

That being so, if "local none" referred to the absence of reporting restrictions, it would be redundant, since to the extent that this is determined by the nature of the alleged offence, the latter is clear from the CJS code: PU86004 means Section 4 of the Public Order Act 1986. Besides, this sequence, "H.O. 125/11 local none CJS PU86004", is what appears on the police charge sheet, and reporting restrictions are a matter for the court, not the police or the prosecutors. And above all, it makes no sense for "local" to refer to reporting restrictions, since if the latter apply, they apply to all media, not just the local press. There will never be a case where particular reporting restrictions, or their absence, apply specifically to the local media and not other media. So "local" would not be used to refer to it.

I haven't found any clear evidence of what "local none" means, but I think it very probably means that there is no local code for this offence.

H.O. refers to the Home Office Counting Rules for Reported Crime. For the purposes of compiling crime statistics, each type of offence with which someone is charged has an H.O. code. H.O. 125/11 refers to:
"Fear or provocation of violence
Public Order Act 1986 Sec. 4"
Home Office Counting Rules For Recorded Crime, April 2010
Violence against the Person
http://www.unodc.org/documents/southeasterneurope/cards-bosn... (p. 72)

As I have said, the third element, CJS PU86004, is another offence code for the same offence. For an explanation of the CJS offence code system, see p. 33 of this document:
HM Government
Criminal Justice System Exchange Data Standards Catalogue
https://www.gov.uk/government/uploads/system/uploads/attachm...

So it seems very likely that since HO and CJS are both offence codes, the same is true of "local", which comes between them. For certain types of offence, especially traffic offences, local police forces use their own local codes, which serve the purposes of compiling local data. If it says "local none" (which it does in all the examples I can find on the Internet), this would mean that there is no local code for this offence.

"The codes that you have requested information for are used specifically by the DVLA, police forces use what are called CCCJ national codes, which are then converted into local offence codes."
http://www.bedfordshire.police.uk/pdf/Response Letter 2012-0...

"None" does mean that there is no code for the offence. This is clear from the following example:
"H.O. None/None Local None CJS BA76005"
This is for an offence under Section 7 of the Bail Act:
"Arrest by a constable for breaking/likely to break bail conditions - this is NOT an offence"
http://united-races.blogspot.com.es/2011/10/racial-warfare-i...

Not an offence, in this particular case, means not a reportable offence. So it has a CJS code, referring to the statute, but no H.O. Counting Rules code, because it is not included in the crime statistics.