The new laws regarding restricted movement are contained in The Health Protection (Coronavirus, Restrictions) (England) Regulations 2020 - www.legislation.gov.uk/uksi/2020/350/made
See s.6 specifically.
S.7 deals with restrictions on gatherings.
I agree we should act in the spirit of the new rules, limit contact with others and practice social distancing and careful personal hygiene/ hand washing etc.
This may all last quite a long time. We have just seen some extraordinary new legislation passed with very limited scrutiny curbing our personal freedoms.
I can see that such powers may be necessary because some people won't accept that the rules apply to them, however we have already seen overreach from some police forces reported in the news. While I agree people shouldn't be selfish and unreasonable, neither should the police be shaming people on social media for acting in ways that 3 days ago were totally fine, and aren't actually in breach of the new rules/ laws anyway.
You are allowed to leave your home with reasonable excuse. The examples listed in the legislation are not exhaustive. It doesn't actually say you can't drive somewhere for your walk/exercise, though of course people should use common sense. There's nothing about "only essential trips"' which is a phrase I've seen bandied about, although the right to leave your house will likely be subject to a test of 'necessity' (for reasons outside of the non-exhaustive list in s.6)
David Allen Green has an explainer here: tinyurl.com/s7p2guz
I respect the difficult position the police find themselves in. We shouldn't however be expected to be treated like criminals in this situation either.