Bus departed 16 minutes early leaving us stranded during the night in Leicester bus station! Complaint response exceeded National express timeframe and resolution was a poor partial refund. We had pre booked two tickets from London Stansted to Derby. Stansted departure at 1730 with a change required at Leicester to depart for Derby at 2035. However, in the process of finding the correct bay to change coaches, we were shocked and what appeared to be our booked bus, driving out of the bus station at 2020. This was over 15 minutes early! The live bus station timetable was also updated, to reflect no National express bus now due at the original 2035 time. We had clearly followed National express advice of "Aim to arrive at the coach station at least 10 minutes before you're due to depart". We now had to try and deal with the added stress of travelling back from Stansted Airport. Now after sunset, trying to make additional travel arrangements inside a dangerous bus station in Leicester at dark. We had to commit to a taxi journey at cost of £36.40. In addition to our bus tickets which already cost £54.91. Which we were left stranded after dark in Leicester. The online bus tracker also confirmed the bus left 15 minutes early and the onboard CCTV should also confirm this. I'm aware as standard tickets, if we were late for a booked journey, we wouldn't be able to just travel on the next bus. We'd then need to buy additional tickets at further costs.