I have lost two pepper plants (one chilli, one sweet) by the plant stem turning black (rotting?) about half an inch up the stem on plants which are about 8 inches high. It's not damping off, I think, but looks just like blackleg in potatoes. With peppers belonging to the solanaceae as well, I wonder if indeed it IS blackleg? Any thoughts?

Do you have to pot these in a bigger pot soon Monika? Try adding some rootgrow to the compost this will help the remaining plants root system and general immunity. I have never seen black leg, but it sounds like you are thinking on the right lines. Hope your remaining plants survive!

I've never had this happen & have been growing peppers & chillies for a number of years so cannot guess how it has occurred unless they're in a greenhouse when some other different plants may have been suffering from it.
I was wondering whether a weak liquid fertiliser like Tomorite would strengthen the plants - rather along the lines of NB's suggestion, and possibly trying to keep the other plants well away from each other, possibly in some different locations, to try and prevent any cross infection in case it's some kind of other disease.

So far it's only been two plants out of ten so, hopefully, it will stop now. I will certainly try your Rootgrow suggestion, NB, and keep them further apart, Primrose. I think one problem must be the cold weather as well - today we had only 5 degrees maximum temperature outside and 10 degrees in the greenhouse with the small electric heater on. It's the strong NE wind which whistles down the moor straight into our garden!

Peppers & chillies certainly don't like low temperatures. I wonder if it would help to keep a light fleece cover over them when the temperatures are dropping down this low. If nothing else it might help to protect their immune systems a little better & help them resist any diseases which are floating around.