I did that route 3 times last winter, twice without incident. On the 3rd we were delayed roughly 1 hour at Dalaman & were met at the gate in Istanbul by a Pegasus lady, who told the Stansted flight had left without us (around 14 people), & that we would be put into an hotel overnight. It wouldn't have been so bad except that we could hear calls for boarding for the Stansted flight. To make matters even worse, they attempted to put us on the evening flight, & not the morning one, from Istanbul the following day. We strongly suspected that the Stansted flight was overbooked & it was easier for them to bump us off the flight.
I think it's fair to say we kicked off big time & demanded that they put us on the (Sl)Easyjet flight to Luton that evening & that Pegasus foot the bill for the difference in price.