Well, I live in the USA and Here you have to be aware of temperature changes from season to season. Now I lived in England up till I was 15 years old and if that is were you are then unless you are going from southern England to Scotland I don't believe that will be an issue.
There are however a couple of things that caught my eye.
1: Are you moving from water that is soft or hard to a place that is opposite that?. say Hard to soft or whatever. In any case some fish prefer hard water, but since gold fish are much hardier than Koi that might not be to much of a problem if you release them the right way which I'll describe in a bit.
2: I would get a inexpensive test kit to check the water at both areas. You can get a kit that has a paper strip in it that will tell you some important factors. Those being Ammonia, Nitrite, Nitrate, hardness, PH which BTW: can tell if the water is HARD OR SOFT. Hard water will always be on the high side of 7.5 PH. That is it will show alkalinity to it and Soft water will be on the acidic side. The water here is 8.5 to 9 PH and is hard and that is due to the minerals (calcium and magnesium are 2 of them), the water has flowed thru, If you are in an area that is made of peat then it will likely be soft water and acid. Anyway with the kit test to see if there will be a major change in any of the areas that the kit will test for.
3: Water flowing in from an outside source is a concern in this day and age due to run off from fields or other places that may bring harmful chemicals into the pond you are moving to. Also you will have to worry about the flow. If a heavy rain storm hits will it send a lot of debris and mud down? Will it possibly overflow the pond and take the fish with it?
If that all seems OK by you then using a container draw water from the original pond, catch your fish and head to the new pond. On this, be sure to let the container be able to get oxygen in to mix with that water for the fish to make a long journey. If you take a peek at them every so often just be sure they are not at the surface gasping for air. If so a gentle agitation of the water will help to draw oxygen into the water for the fish.
The toads will be no problem as long as they have a few nice spots to make them selves a home close to the pond. A few rocks that have a few inches space beneath them and the ground is a good start or just form something that resembles what they life in/under now.
Finally, when you get the goldfish to their new home let the container sit in the pond water for a time to equalize the temperature between the bucket/bag that the fish are in and the new pond. Lastly don't just pour the fish in, mix a bit of the new pond water in with the old and continue to do this at short intervals . This way they are not "shocked" by a dramatic water change.
That's all I can think of at the moment but it's 11PM here and I'm off to bed. I'll check back and see if you have any Q's I didn't address and also any5thing else I need to say...Don't worry I have hit the most important ele3ments on this, but I'll think some more.
Good luck
Oh the Lillie's should be fine if the water and temperature of the new area. With that constant flow and I am guessing a certain amount that is leaving via the ground the water will not have the same feeding ability as the enclosed pond since fish droppings feed the plants and the plants give oxygen and help clean your water. I have 8 or so in my large pond and you may want to get small feeding sticks that press into the are around the Lillie but only give a Small amount to feed the plant and not put phosphates or other things into your water.
The toads will enjoy a cool container that is damp and has some natural vegetation put in with them to help, Being cold blooded they need to be kept at a even comfortable temp as they might have difficulty regulating there temperature as they do out in nature.