CLSG is a fine school, but there are other fine schools closer to you. Four years ago, we were in a similar position living in a North London suburb. But we decided we were not happy about the safety of the commute and, quite separately, we did not want our child to spend so much time and energy commuting. ( One of us commuted a lot as a kid and still regrets its impact.) We also wanted her to have mainly local schoolmates. So we applied to NLCS and others in NW London, as well as HBS as a grammar school.
For four academic years now, our DD has done a lot of extra curricular and after school activities, both at school and locally: they mean the world to her, she's made different groups of friends through them and they have offered her extra dimensions of growth, challenge and fun. And she still has time to keep up with studies and, of course, lots of social time and some down time and some Grandma time, too!
Although SleepyHead makes a valid point, those extra hours of time and bundles of energy freed up by not commuting - every day - are priceless.
Finally, warmest congratulations to you and your DD on earning such wonderful options.