In English we call the season now in Japan the rainy season (梅雨). One of the main symbols of the rainy season are the beautiful Hydrangea (アジサイ) that flower at this time of year.
The U.K. doesn’t have a rainy season but is famous for being a wet country. It actually has an average of about 130 rainy days a year, which is nearly the same as Japan. However it is fair to say that the weather in the UK is certainly very changeable (変わりやすい), often with many different kinds of weather in one day.