On our trip to London this spring, with a side trip to Sardinia, we wound up flying into both airports. The HEx (Heathrow Express) offers early bird online fares for £15 per person each way, and the GX (Gatwick Express) offers a 10% discount if you buy tickets Online, so starting at £21. If you’re planning on doing more train travel on your trip, consider getting a Two Together rail pass, and you can cut those prices further.
The HEx gets into central london at Paddington Station, northwest corner of town, in about a half hour. The GX arrives at Victoria Station, southwest, and closer to Trafalgar Square, but in about an hour. If those locations make a difference, Gatwick would seem better.
If time is important, a few minutes either way, on our last flights, we had a shorter walk at Gatwick to reach immigration/border control than at Heathrow, but I don’t know where at either airport your Icelandair flights will dock, compared to our flights. Heathrow was also a LOT busier this time, with a bigger crowd to get through. So that all could affect overall commute times.
Are the schedules really the same - two flights departing Reykjavik for different airports in London at the same time? When do the Heathrow and Gatwick flights land, and with the commute factors, will that make a difference in your hotel check-in and sightseeing schedules? That might be the biggest determinant. Also, does either flight actually involve a longer layover in Reykjavik?
So everything else being equal, with Heathrow being closer to London, and with a little cheaper and quicker early bird commute price, Heathrow would be preferable. If arriving at Victoria Station in London via the Gatwick Express is better in the end, go with Gatwick. In the end, it might not be a big deal either way.