Since you have live plants in the tank, adding ammonia (which is the way to cycle a tank without plants) is not an option.
The plants you have are quite small at the moment, you need to wait until they grow a bit more. Getting floating plants will help a lot too.
Do you know about the nitrogen cycle? At the risk of saying what you already know, fish excrete ammonia, which is toxic. Bacteria grow in the tank which 'eat' ammonia and turn it into nitrite. This is also toxic, but another type of bacteria grow in the tank which 'eat' nitrite and turn it into nitrate. Nitrate is less toxic than the other two but needs to be kept below 20 ppm so we do water changes to remove it. Fishless cycling is where ammonia is added to the tank before fish are added to grow these bacteria ready for fish.
Plants take up ammonia as fertiliser and they do it faster than the ammonia eating bacteria. If there are enough well growing plants, they will take up all the ammonia made in a sensibly stocked tank of fish. Floating plants are near the lights and can get carbon dioxide from the air so they are particularly good at removing ammonia. Using plants to remove the ammonia is called plant or silent cycling.
Since you already have plants, you have started a silent cycle. Wait until they are growing well and not about to die - and I do suggest floating plants as well. Then get the first batch of fish. Buy a test kit - or at the least, testers for ammonia and nitrite - and test for those every day after adding fish. If either show above zero, do a water change. Once you know they are staying at zero, and the plants are still doing well, get the next batch of fish.
In the meantime while you wait for the plants to grow, get a test kit and research the fish you want to get. The first stage in research is to look on your water company's website for hardness. You need a number and the unit of measurement rather than vague words. As UK water companies often use units different from the ones fish keeping uses, post your hardness on here and if necessary we can convert it.
The reason for this is that fish have evolved in water of a certain hardness. If we put hard water fish in soft water they will suffer from lack of minerals; if we put soft water fish in hard water they get calcium deposits in their bodies. Neither will live as long as they should. It is better to keep fish which come from the same hardness as our tap water.
I've thrown a lot at you all at once. We can talk about which fish are suitable for your water and tank in another post