@aidan,
So 'around' has multiple, sometimes overlapping meanings:
Approximation of time, place or quantity:
I'll meet you around six o'clock
On our journey it grew dark somewhere around Albuquerque
He owes me around six hundred pounds
I weigh around twelve stone
I've seen him around Notting Hill
Neighbouring or bordering:
"Satellite towns" are certain towns around London such as Stevenage, Watford and Croydon
Surrounding:
There is a belt around my waist
The seas around Britain
If I use 'around' with a definite article - the counties around London - I mean 'those counties which together surround London'. If I use it with no article - counties around London - I just mean 'one or more of the counties adjacent to London'.