Algae is an opportunist. It will use any imbalance in the light/nutrient balance to increase. Higher plants are much more demanding in their light and nutrient needs. In a new tank, the biological balance is not established, and the algae has a decided advantage.
There is a lot of "balance" here. A new tank will cycle, but this is only the beginning. Once it is cycled, it was establish which takes usually a few months. Water parameters and water conditions will sort themselves out, and after a few months the tank is deemed to be "established." This is why for many fish, especially small or delicate species, it is often suggested that they be added to established or mature tanks; such fish can be seriously harmed by fluctuating water parameters and/or conditions.
Knowing the parameters (these refer to GH, KH, pH and temperature) and conditions (these are ammonia, nitrite, nitrate, and any other relevancies) along with the light data including spectrum and duration can help fine-tune.
With respect to the plant in the photo, that is a Cryptocornye species. They are very temperamental. It would be better in a sand substrate, but that is not the issue. Plants need light and nutrients. The latter is going to be lacking in a new tank as I referenced above, so you should consider fertilizer, and here with a plant rooted in the substrate, a good substrate tab will be ideal. Flourish Tabs were what I used; the API tab is not as good, but there may bee others in the UK.