A number of flights to Africa and South America depart during the evening too - 12 hour flight means they get to arrive in the morning at those destinations. If you are 4 miles southeast of Heathrow and they are passing overhead, it is these flights that you are seeing as they turn right and leave the UK in the area of Seaford, near Brighton.
Far East-bound flights usually turn left after take-off and leave the UK over Clacton whilst others fly out over Dover. The exact routes used depend on the airway structure but also on the flow control restrictions at the time.