I think this container is about 80 litres. It is the biggest I have. Do I rinse the filter sponge in old tank water first? Or do I just move it over? I last rinsed it 2 days ago.

I would just move it straight over, it doesn't really need rinsing and you want to preserve as much good bacteria as possible

__________________

It turns out the container is 60 litres but I got 52+ into it. I have moved the filter and the fish and it looks happier already. I am waiting for my camera battery to charge so I can post a pic but I am fairly sure now it has ich/white spot.

That's brilliant, 52 litres is a loads better than 17
If possible it would be a good idea to buy yourself a test kit so you can keep a close eye on water parameters. Something like the API master kit would be ideal, but whatever you do don't waste your money on the cardboard test strips as they are very inaccurate.

__________________

I was unable to get a clear photo but I wrote down all the details and went to an independent pet shop. They suggested Medica+ Lifeguard because I was describing symptoms of white spot and the fuzzy cottony stuff. I also bought a test tube water testing kit. I have tested the water in the plastic tub and all is as it should be. I also tested the 17litre aquarium and, surprisingly, the water there was fine, too. This is likely because I had performed 25% water changes 3 days in a row, so the damage probably happened prior to this. I was becoming more worried before I left the house as the fish was looking a bit slow, but since I came home it is swimming around beautifully, not just in reaction to me coming to the tub. I know we are not anywhere near out of the woods but I am much more hopeful than I was last night. Looks like it will be staying in the plastic tub until we can get a bigger tank, all being well.

Phew, I never thought goldfish care was so stressful, I barely slept last night and I haven't eaten yet. My five dogs are easier cared for......

Thanks for all the help.