I have spotted that one - and only one - of my peppers plants has a number of small black flies of some type hanging around the soil. And while writing this I've just spotted that one (and only one!) of the leaves has what I guess might be aphids on the back of it. So I'm now even more concerned than I was.
I first spotted the bugs 2 or 3 days ago, and it's definitely the case that the black flies are living on, or around, the plant given their behaviour and location. They are most often walking around the soil or pot, occasionally sat on the lowest leaves.
The plant seems healthy at the moment (as much as my negligible experience can tell) and doesn't look like it's being eaten or anything, but I guess this might not last long.
Note that there is another pepper plant about 30cm away, which is showing no signs of similar pests or anything on the leaves.
What should I do?
Having started doing research on the web, can I just say that the plants are indoor potted plants and I have no external garden whatsoever; introducing another insect that will eat these is not possible.
Here are some images to hopefully help:
One of the bugs sat on the pot by the soil line:
And the back of one concerning leaf: