London climate is influenced by Atlantic currents, and during spring the weather can change really fast. In March you can still see some snow and even frost. However daily temperature rises, and there is more sunshine to cheer you up. A few warm days can be followed with the return of winter weather.
In April it can still be as cold as during winter, even though there is more sunshine and days get longer. May is the first really warm month of the year. However, rains also return along with the warm fronts. While March and April are relatively dry, May gets more precipitation and humidity.