Since this seems to be a forum for getting the facts right, I think it was always called Honor Oak Station (without a 'u') as in the current name of the area. Having said which, the 1870 OS map calls it Honour Oak Station - but it has changed to Honor Oak by the 1894 edition!

We are almost certainly looking at the back of the train as it is leaving Honor Oak Station - trains nearly always run on the left in the UK. That being the case it is very difficult to see whether it is a steam train.

Wikipedia (here) says that this line was electrified in 1925 so the picture must be older than that. That being the case it seems probable that the train in the picture was steam hauled. I can't find any evidence that diesel engines were ever used on suburban railways pre-electrification. The Southern railway was initially electrified using overhead ac power. Perhaps we would have less problems in bad weather if it still was!