OK, so it's quite complicated really.So how does it work with licenced mobile slaughtermen? fact is a mobile slaughter man can come to you and kill on your premises for you to use the meat, he is not allowed to dress. Likewise he can turn up with a mobile abattoir and kill infront of vets and prepare the animal for sale.
You are correct in so far as it's not legal for a slaughterman (or anyone else) to come onto your premises to kill and dress a carcass, even if it's only for your own consumption. This is because, in the eyes of the law, you supplied him with a live animal and he supplied you with meat that had not been slaughtered in a licensed premises.
The next bit is a grey area. It may be legal for someone to come into your premises to kill an animal for your own consumption, provided that he does not assist in anyway with dressing the carcass. This is because, in the eyes of the law, he may be deemed to be providing a service, rather than supplying a finished product. But the law is not entirely clear, and in all likelihood you would not get away with it, and if he was a licensed slaughterman he may lose his licence for operating outside of a licensed premises.
(The law in Ireland is a bit clearer, and I think it would be OK).
A mobile abattoir can only operate on a licenced site. So, where such an abattoir is owned by a syndicate of farmers, each will have a designated concrete pad with appropriate drainage etc upon which the mobile abattoir must be parked when operating on their farm. So a mobile abattoir can't just rock up on any farm or smallholding. Which is a pity, because there'd definitely be a market for it.
(I think the rules may be a bit different for poultry only mobile abattoirs, but I'm not sure off the top of my head).