Just booked the trip for the five of us! I found that Iceland air is considerably cheaper than other options, and the layovers in Reykjavik are reasonable -- 1 to 2 hours. Of course the trip over will be brutal -- leave at 9:30 pm, 5 hours in the air, then land, layover for an hour and get on another plane. But the trip over is brutal when you land at 6am London time too, so it is what it is. At least we'll be able to check into a hotel as soon as we get to London, and not have to wander around with our bags! And take a cost increase of $100-200 for a better (i.e. nonstop) flight and multiply it by five, and you'll see why I'm willing to do it this way. I considered a longer layover in Iceland, but decided against it. We'll have enough to do in the UK to fill up our 10 days.
We'll do a little London, maybe Oxford, the old walled city of Ludlow in Shropshire, with a side visit to the Roman ruins at Wroxeter, and hopefully some coasal Welsh castles. Recommendations appreciated, and more to follow!