The largest biz-jets that currently operate from LCY are the Global Express series and Falcon 7X. The ACJ and BBJ aren’t steep approach equipped, the only Airbus certified to operate in their is the BA A318 which was modified for steep approaches.
Weather can make a huge difference, low QNH, high temperatures and not much wind can really limit take off weights. Generally runway 09 is better than 27 as there’s less obstacles.