We stayed at Alex's wonderful flat with our two kids (ages 7 and 4.5). It was absolutely perfect; everything was exactly as described. Alex was flexible with checkin, allowing us to drop our bags off early. The pantry and fridge had an over-abundance of food, which made for easy breakfasts and let us prepare lunch to take with us. We could have made dinner at the flat if we wanted to, though Alex provided many restaurant recommendations.
Alex's instructions for finding the flat were clear and easy. It's a short walk from the Tube and many bus stops. Combined with the mobile phone Alex provided for use during our stay, the proximity to transit made our day trips painless.
The rooftop terrace is peaceful even with a busy street below. The neighborhood seemed very safe, and includes lots of restaurants and shops, and a small open-air market with food stands. "Wicked" and "Hamilton" are about a 10-15 minute walk away.
In short: you should stay here if you can. If we return to London, we will make every effort to do so ourselves.