Oh Dear Andy youve picked a good one mate what do we have a fungal infection or Columnaris
Both are very simmilar are brought about by a number of factors from water quality parasite attack or water temperature fluctuations poor diet etc, fungal wise or as the lack of the dorsal fin points to Columnaris
If its columnaris you need to take a swab of your fish to send it off to identify which bacterium your up against then treat your fish accordingly as per instructions your dealer or your veteranarian will be more than happy to help you in this even idenifying the bacteria for you suggesting which would be the best antibiotic for this problem
If fungal then your point of entry most probably will be a parasite comlicated by the other things I've already mentioned so then your going to have to track down how and why .
For heacily infected fish remove sedate and treat using a cotton bud at a time to remove any fungus then paint the area with Malachite green then spray with propolis to finish off your going to have to sedate your fish to do this , if you cant get your hands on propper fish anethetic such as MS222 then Oil of cloves at a rate of 10ml per 2 imperial gallons will suffice , the trick is to wait till your fish is totally under before you treat once this is done hold the fish in the pond near an airiated flow until you feel the muscles kick back in and release we take heavily infected fish out owing to the number of fungal spores that they can release which we dont want.
once this is done and wounds are treated we can then go about treating the pond for this your going to need a top of the range anti fungal treatment repeating if necessary
Aproximately how many are infected and are they just yoour koi not the goldfish ?
What is your water quality like ammonia, nitite, nitrate, ph ,kh and gh.
Is your pond over crowded are you getting temperature fluctuations when was your last water change what was the last parasite you treated for Questions Questions but all need answering if your going to win this battle.
This is why I'm so hot on prewinter maintenance of pond and filters and why I carry on throughout with routine water changes winter otherwise is a time of mistakes and we shouldnt be making them, this may very well be an expensive leason for you should you suffer losses .
Best of luck in your treatment of
PS if you still lived in Crownhill Andy I could have popped up to help you mate
Dave