A rain jacket is essential, as is a small backpack to carry it in when the sun comes out. In summer, you'll need sunscreen and an umbrella; you’re bound to use both – possibly on the same day.
For sightseeing, comfortable shoes can make or break a trip. If you plan to enjoy Britain's great outdoors, suitable hiking gear is required in higher/wilder areas, but not for casual strolls in the countryside.
Some bars and restaurants have dress codes banning jeans, T-shirts and trainers (sneakers or runners).