How long will it take chilli pepper plants to grow to fruit? How fast do they grow?

OK, simple question, simple-ish answer. Based on my experiences for "normal" chillis (those with scoville values under 100k):

Seeds: 

Germination is variable but usually within a week you have "green shoots", though it may take longer if you planted them deeper (I always plant VERY shallow)

Seedlings:

Roughly 0.5cm a day is a reasonable expectation.

Small Plants: 

About 15cm a month vertically, though they also spread outwards, usually around the 20-30cm mark they will fork into a Y shape and then I class them as larger plants.

Fruits and The "Y fork" at around
2 months old / 30cm
Cherry Bomb Pepper

Larger Plants: 

About 30cm a month vertically but they do really start to go wild sideways at this point.

Flowers: 

Buds usually start appearing at about the 20-30cm mark, usually around the same time as the Y shape fork. Few at this point, maybe 3 or 4 buds. These take about a week to open, sometimes a couple of weeks

Fruits: 

Usually somewhere around a week after a flower opens it will go brown and either drop off, or the petals alone will drop off leaving the stump behind, which has a slightly swollen tiny tiny pepper blob (this is green). This will then swell over the coming weeks.

Ripening: 

Depending on how you want to eat them - usually to grow to full size takes 2-4 weeks (longer for the bigger peppers) and to ripen can be a fair wait if you want to go all the way to the final colour (usually red). Some peppers can take 4+ weeks to ripen, it can feel like an age. But others can do it within a week or two.

Summary:

So, total time from seed to the first edible fruit, a MINIMUM of 2.5 months. Which to be fair, isn't long. Realistically though, the average would be longer, maybe 3-4 months. And for the real harvest which comes later, another month or two.

In the UK, you're supposed to sow seeds early spring, some sow as early as January (indoors obviously!). I have sown as late as June and had success.

I do plan to try some in winter to see what happens. Just out of curiosity really! Will let you know!

Note that I don't really grow any of the high scoville peppers at the moment, I know they are particularly slow growing and stubborn. So if you plan to grow a Naga or similar, expect a much longer wait! 

Hope that helps!