“Milky water”, when aquarium water turns a translucent white, is a common occurrence in new aquariums or when gravel is stirred up, for example when one moves it from one aquarium to another one.
A bacterial bloom is caused by a sudden increase of heterotrophic bacteria due to release of organic matter from the gravel or the sudden dechlorination of large amounts of water, which allows bacteria to multiply.
So it was no surprise when the water in the new aquarium became cloudy.
There are a couple of ways to combat a bacterial bloom in an established aquarium: water changes and patience. I opted for the latter option because there was no readable amount of ammonia or nitrite in the water and water changes on a 420 litre aquarium are not that easy to perform.
In general, the likelihood of a bacterial bloom in an established aquarium can be reduced by cleaning the gravel regularly, but I prefer to leave everything to decompose naturally as I do not have a nitrate problem and the plants do need food.