I have always found that a hot cup of tea (no milk) and not particularly strong helps me to sleep. Perhaps its just the warmth. Same if you wake in the middle of the night.
One side effect of drinking a long-brewed cup of black tea (a good side effect) is it makes you sleepy and induces deep slumber. A tea bag of black tea should steep for 10 minutes in a cup of very hot water to get the sedative effect. The tea undergoes a chemical change when brewed for 10 minutes. Most people only brew the tea for 3 minutes which creates a stimulating effect. I usually dream in my sleep after drinking a long-brewed cup. Dreaming is the sign of a deep sleep. The soporific effect of long-brewed black tea is well-known to marathon runners.