Welshlass,
The links you provide are not contradictory, just written by the FSA and others who don't want people home killing, so are phrased to persuade you not to !
The first link is the welsh guidance, which says you cannot pay a slaughterman to kill and dress, but does say under para 23 that the farmer can kill the animal himself.
The second link (Welsh government) repeats the same ie farmer can kill the animal himself, otherwise must be licenced slaughterman. The fact that this part does not state anything about consumption is just that it is covering killing, as are the 1995 regulations. Both these are just about being able to kill an animal, so don't cover the private consumption.
What is interesting is that the FASA 2011 guidance says
"It is unlawful for a farmer to use the services of an itinerant slaughterman both to slaughter his animal and to dress it. This is because the slaughterman would be supplying goods (i.e. a dressed carcase) in the course of his business."
whereas the same FSA guidance in the 2009 version stated
"It is unlawful for a farmer to use the services of an itinerant slaughterman both to slaughter his animal and to dress it. This is because the slaughterman would be supplying goods (i.e. a dressed carcase) in the course of his business. However, if the slaughterman did no more than kill the animal, leaving the farmer to dress and cut the carcase, the Courts might be less likely to conclude that the slaughterman was supplying goods (and more likely to be supplying services). If so, this activity might be held to be lawful, (i.e. the EU Food Hygiene Regulation 853/2004 would not prohibit it) although the issue is far from clear. The EU TSE controls would in any event apply."
The revision history of these documents states that the difference between 2009 and 2011 is "To reflect alternative arrangements for BSE Testing", so whilst TSE species are far more difficult (pigs are not in the TSE group), it looks like someone has made the decision to edit out the second part (no doubt on the grounds of being clear) and make it look as though any use of slaughterman would be illegal.
However in all cases, this would be for consumption of "immediate family living in the same household", and any "placing on the market" - eg giving or selling to anyone else would make that placing act illegal (although the kill could still be legal).