Ensure you have adequate clothing. Wearing layers of clothes is a good way to keep warm, wearing a T-shirt under a jumper for example. You can buy thermal underwear in the UK which is very useful if you tend to feel the cold - particularly advisable if you come from a country with a very warm climate. You will need a warm heavy coat for winter and also a waterproof jacket or coat. An umbrella is also very useful.
Spring can be very changeable.
It can be wet but often has some lovely mild weather. This applies to Autumn as well. English Summer has a reputation for rainy weather. Although this can be true it can also be very warm. A warm sunny English summer day is truly enjoyable.