This is interesting, as is almost all legislation in all countries. So an intentionally non-lethal weapon is more tightly restricted than 'proper' but fully lethal weapons. And apparently cattle prods and electric fences are not used in the UK cattle industry.
Electric fences, yes those are in use; but that's hardly a portable 'weapon'. An electric cattle prod could be, but I have never seen one in use in the UK. Just not British stuffing 10 kV up Daisy's bum. A slap on the backside and "Move along ol' gal" is more Farmer Brown's style.
That said, the advice for crown prosecutors says that cattle prods would not normally be treated as prohibited weapons for possession offences. Where one was deliberately used as an offensive weapon then I suspect that a sensible view would be taken as to whether the use as a weapon was merely incidental in innocent possession of the device (say, a farmer on his own land), or whether it was acquired with intent to use it as a weapon, where I imagine a possession offence would probably be charged.
The history of electroshock weapons ending up as Section 5 prohibited weapons is interesting. Originally electroshock weapons were not legislated for. The part of Section 5 used to cover them applies to "5 1 (b) any weapon of whatever description designed or adapted for the discharge of any noxious liquid, gas or other thing" and was originally written to cover the use of water pistols filled with ammonia solution, an old bank robber's favourite when ammonia was a common household chemical and, if caught, avoided a prosecution for robbery with a firearm. Thus the intent was to treat this tactic as seriously as a real firearm. Then someone somewhere used an electroshock weapon and case law decided that electricity could be a "noxious liquid, gas or other thing".
As to "intentionally non-lethal weapon" - given there are reported deaths from the use of electroshock weapons I think we can only accept "less-lethal". And further, as to "more tightly restricted than 'proper' but fully lethal weapons", I think it's closer to say
as tightly restricted as more lethal weapons for all
practical purposes. Remember, the only real firearms that a 'civilian' can lawfully possess in the UK are single shot target or hunting rifles and single and double barrelled shotguns. No handguns and no repeating weapons, and all weapons and all ammunition require a license which will
always carry conditions on where weapons are stored, where they are used and how much ammunition may be purchased or possessed at any time.
To put things into perspective, there were in March 2015 582,494 shotgun certificates and 153,603 firearm certificates covering 1,338,399 shotguns and 525,125 firearms in existence. That covers every farmer, pest controller, sporting shooter and shooting club in the country. Even spread out among the population that's one 'firearm' for every 34 people and some 'firearms' that might be covered by a certificate are not what one might traditionally think of as a firearm such as a line throwing gun. In practice, regular contact with, or experience with, firearms is much, much less common than that 1 in 34 overall figure might suggest. Basically, 'proper' firearms are exceedingly rare in the UK.