ENGLAND & WALES
This comes under the
In England - Pigs (Records Identification and Movement) Order 2011
In Wales - Pigs Records Identification and Movement Order (Wales) 2011
Part 4 Para 15 states :
"15. A keeper moving a pig to a veterinary practice for emergency treatment need not notify the movement. "
So you don't need to notify if you deem it an emergency.
As stated there is an option under e-aml2 to do a move to a vet, this would be for non-emergency treatment, although of course there is no reason why you shouldn't notify all moves to a vet - just that for emergency you don't legally need to do so, and care of the animal comes ahead of paperwork!
In E&W, you'll still need the correct ID ie temporary mark if under one year, and tag/tattoo if over 1 year (compare with Scotland below!)
SCOTLAND
In Scotland it comes under - Pigs Records Identification and Movement Order (Scotland) 2011, and the rules are different !
Para 12 requires you to notify information to the Scottish Ministers, either prior to the movement or on the day of the movement, but does not exclude veterinary treatment, so yes you would need to notify, but of course in Scotland you can do this afterwards as long as on the day, so emergency treatment is covered as you can post notify.
However para 14 excludes the need to ID a pig - Para 14 states :
"Any provision in this Order requiring the application of a means of identification to a pig before it is moved from a holding does not apply if the movement is for the purposes of veterinary treatment. "