Customs in Iceland

If this is one through booking, the following will happen:
1) Your baggage will be labelled through to London, you will first see it there.
2) You will stay airside in Iceland. You will not legally enter Iceland.
3) When you land in London (make sure you know which airport, London has 6), you will go through immigration (passport control). This could take 30-60 minutes depending on how busy they are.
You will then pick up your bags and carry them through customs (through the green "nothing to declare" door). This is a random spot check only, unless you are very unlucky you will not be stopped.

You have posted this in the England Forum. There is an Iceland Forum at https://community.ricksteves.com/travel-forum/iceland

First, you have plenty of time. Second, I hesitate to disagree with Chris F., because what I've observed, he is extremely knowledgeable and a great resource. My first trip to France was on Icelandair and we connected through Iceland. I do recall going thru some kind of immigration. We presented a passport to an officer in a "booth" and then proceeded thru to our next gate for our flight to Paris. I recall having my suitcase, but I'm pretty sure that I had carried it on. I remember all this because it seemed to be so unorganized. Since then I've realized that the airport is so beyond capacity due to the increase in numbers of flights.

Jules, If you were flying to Paris the procedure would be different.
Both Iceland and France are in the Schengen Area. You would enter the Schengen Area in Iceland, have your passport checked and, if you are a non-EU/Schengen foreigner, have your passport stamped.
Iceland-France is a Schengen internal flight, no passport checks on landing in Paris.
You would still pick up your bags in Paris, and carry them through customs there.

The UK is not in the Schengen Area, so you can stay airside at any intermediate stops, and enter the UK when you land in London.

Chris, thanks for the explanation. I didn't know GB wasn't in the Schengen Area. I figured because they are in the EU (for now) that was synonymous with Schengen. I learn so much from this forum!

Thank you so much for the information. My mind is a little more at ease knowing that it should go pretty smooth.

Joseph, we just did the same trip a couple of weeks ago. You have received excellent advice here. Only thing I wanted to add is that the Iceland airport can be very crowded and chaotic. You will likely ride a bus from your plane to the airport, then you need to find your next gate. The airport is very small and there are two flights that board at each gate. So, once you find your gate there will be a lot of people crowded around and you need to pay attention to when they board your flight.

If this is your first trip on Icelandair, enjoy. We found the economy seats to be comfortable with plenty of leg room. Make sure you bring your own food. They will serve water and sell other stuff at a very high price.

My experience flying Icelandair to/from the UK in late 2015, convinced me that Icelandair is pretty much the big dog airline at KEF. It's their hub and they make things work for the passengers.

Flying out from DEN to Glasgow: red-eye from Denver landing at KEF at 06:30 (AM). Cabin crew onboard had told us there was some kind of labor action with the border control agents but not to worry, we'd be taken care of. We got in a line - I think we were airside still - which moved pretty fast up to a stand where somebody who looked official stamped my passport twice, once for entry, once for exit. I just looked, I think each stamp has the flight number on it. Then I had time to visit the ladies' room and have some yogurt and fruit for breakfast before our flight for Glasgow boarded. It wasn't a long layover but it was enough.

Coming back, from Gatwick to DEN, our flight from Gatwick to KEF was delayed taking off by something like 90 minutes. Once on board, we were assured by the cabin crew that nobody connecting at KEF would be left behind. It proved true. We didn't have to go through passport control coming that direction. I was one of three Denver passengers who lined up at the wrong gate in a lonnng line, because their signage was screwed up. When I realized the problem, I was immediately put in a vehicle with the other two misdirected passengers, driven out to the Denver plane waiting on the apron, and indeed they'd held the plane till we got onboard.

I would never worry about making a connection at KEF if through-ticketed on Icelandair. In my experience, they will make it work for you.

Edited to add: Both outbound and returning home, I checked a bag at the beginning of the trip and didn't see it again until baggage claim at my final destination. Easy peasy.

Jules, Joseph, This is a map of the Schengen Area (from the EU's own website): https://ec.europa.eu/home-affairs/sites/homeaffairs/files/schengen_map.jpg
As you can see, most countries in the Schengen Area are also in the EU, but some are in Schengen only (Iceland, Switzerland), and some EU only (UK, Ireland).
Which is why you get passport checks (but no customs) between the UK and France, but you have customs checks on commercial vehicles between Switzerland and France (but no passport checks on travellers).

Just to add to Chris's points, the EU, the Schengen area, and the Euro-zone are three different things. There is a lot of overlap - but there are many places in Europe that are only in one or two of these three. And, of course, these things can change (for instance, some countries have adopted the Euro relatively recently).

Suz: you went thru immigration by mistake in Keflavik which may
explain the entry/exit double stamping.

In previous years most flights had jetways and it was clear what was
Schengen (upstairs) and non-Schengen (ground floor). Now with all the
busing and escalators it’s pretty chaotic and you really have to know
what you are doing, when to line up for immigration and when to turn
back.

Whatever I did, it wasn't my "mistake." Everyone on our plane was directed to get in that line, and we did. And when I got to the desk, the official didn't look at my passport and boarding pass and say I was in the wrong place, they looked at them and stamped my passport.

The important thing as far as I'm concerned, is that I made my flight connections at KEF both times.