I long ago gave up on attempting to have a coffee in any of the Dulwich cafes for the reasons listed by MrTwirly. My advice is to jump on a 176 to the Charing Cross Road and go to Caffe Vergnano - there's no wifi and no space for buggies and you will get one of the best coffees in town, a range of great pastries and snacks for less than you would pay in the Blue Mountain or Lucca....outside of the rush hour it's around a 20 minute journey and a small price to pay for retaining your sanity.....