Running in London, suggestions?

Next step after Paris will be London, for christmas and new year.

I will be located in Brixton. I love it and I want to share with my daughter such a great place.
She's used to traveling, but, unfortunately, she has no experience in living with different cultures. And in my exprience, Brixton is a great example of what melting pot means.

I havent found just one good reason not to run in London (indeed!).
So I'm determining best running paths I could do in London.
As for Paris general rules are two different routes:
a small one near Brixton (10/12km) and the long one (20/30 and maybe 40km) maybe starting from Brixton and back, maybe through Hyde Park, Regent Park and so on.

I developed few running paths on gmaps:

1. From Brixton to Streatham Common

View Directions to Streatham High Rd/A23 in a larger map

2. From Brixton to Kenninton Oval

View Directions to Kennington Oval in a larger map

3. From Brixton to Hyde Park

View Directions to Serpentine Rd in a larger map

Does anyone could submit any suggestion, propose alternative running paths or any usefull infos?
as always, thanks in advance!