This are is complex and every TS seems to explain things differently [ie make up different rules].
Of course if you work in TS, you'll want people to register and do the full thing as 1) you'll have seen cases where for instance bad storage caused illness, 2) the more who go through this process the more likely that you'll keep your job and 3) If you told someone they needn't and then they cause an illness outbreak, you'll get blamed. So nothing in the system will get you a "don't need to" answer if you ask officialdom.
This is not an area of my expertise so below is just my understanding, but in general there are two seperate issues here.
1. public vs. private sales
If you advertise then this is a public sale, and you'll need to be registered as a food business, and comply with various regs inc Food labelling regs, and correct storage and transport.
If you sell privately - ie a private agreement to people you know, then this is just that - a private arrangement not subject to the regs of a public sale. Of course if your meat kills them, still expect to be done !
2. Farm gate sales.
There is a tradition/concept that sales from the farm gate are ancillary antivities to agriculture, so don't come under the same rules as a shop would. However I can find no legislation that states this, and if you are putting boards up saying "pork this friday", then checking with TS may be a good idea.
As others have said if you're doing this regularly, then maybe TS should be contacted, but whilst some TS may be really helpful, others may see this as an opportunity to make you go through hoops!