In reply to OwenM:
I'm pretty sure it's vague on purpose, so the details can be adjusted and announced as appropriate to the circumstances at the time. It wouldn't be a great idea to announce specifics in advance, only to change them at the time.
The main changes appear to be that you can meet with more people outdoors (perhaps changes to the only one family per day recommendation) - so for example meeting up with a few mates or other families to go for a local walk, and that you can also meet up with one other household at a time indoors - so for example have your parents, or a partner that lives in another house, round for socially-distanced dinner; indoor non-office workplaces reopening, some smaller retail reopening including outdoor spaces in pubs and restaurants (bet the weather craps out now...), and playgrounds and sports grounds reopening.
There's no change suggested from phase 1 regarding travel for outdoor activities, which I think is what you're mostly asking about. They might give different recommendations or further clarification as to what "local" means, but they might not.
Phase 3 is the exciting one for us, I think.