The police enforce the law not guidance. This is what the law actually says:
Exceptions: leaving home
2.—(1) These are the exceptions referred to in paragraph 1.
Exception 1: leaving home necessary for certain purposes
(2) Exception 1 is that it is reasonably necessary for the person concerned (“P”) to leave or be outside the place where P is living (“P’s home”)—
(c)to take exercise outside—
(i)alone,
(ii)with—
(aa)one or more members of their household, their linked household, or
(bb)where exercise is being taken as part of providing informal childcare for a child aged 13 or under, one or more members of their linked childcare household, or
(iii)in a public outdoor place, with one other person who is not a member of their household, their linked household or their linked childcare household
So, as you can see, it's all perfectly straightforward and there is no need to define what 'local area' means at all. We simply need to understand what is meant by 'reasonably necessary', which sounds clear enough to me...