Avon and Somerset police have had a few lines on this. The 2 mile area was in one but I can't find it right now. This one is similar:
We continue to receive a lot of questions about why we are advising against driving to beauty spots / popular walking destinations to take your daily form of exercise.
We are following Government guidance in advising residents of Avon and Somerset against all but ‘essential travel’. ‘Essential travel’ has been outlined as: collecting medical supplies, driving to and from work (only when it is absolutely impossible to do so from home), helping a vulnerable relative or friend, and to purchase essentials such as food (as infrequently as possible).
We are encouraging everyone to play their part in the global health crisis we are facing by leaving the house as little as possible. By doing so, you will be saving lives. Please, be mindful that driving to an area away from your home isn’t considered necessary travel (other than for the reasons mentioned above). You are still able to take one form of exercise per day, but we advise you to stay as close to home as possible. When leaving your home, please remember to practice social distancing by keeping a two metre distance from people around you.
Please remember, we are all in this together.
We would like to thank the monumental number of people who are already following Government guidance and staying at home as much as possible. #StayHomeSaveLives.