We stayed in James' apartment for 4 nights in June while visiting London with our 3 kids (age 5, 8, and 13). The apartment was equipped and suited for the family with an amazing roof top terrasse and a very nice living room where we could spend the evenings after the kids went to sleep.
We found the location slightly far away from London city centre - it took us approx 30 minutes with the train and metro. It was definitely manageable, but with the kids it would have been nice to live slightly closer to be able to go back and rest in the apartment during the day. The Limehouse neighborhood is basically one main road with a lot of traffic - however a 10 minutes walk away you find the River Thames and the pubs and restaurants along the river side. One night we had dinner at the Gordon Ramsay's restaurant "The Narrow", which was nice food and amazing view of the river. Two nights we ate at the Turkish restaurant Kirvem recommended by James in the welcome material - and we had a very pleasant experience here - welcoming staff and great food!
Overall a very good experience - however next time going to London with kids we would consider living slightly closer to the city centre.