Warning, graphic explanation so don't read if you're a nervous flier!
I'm a former Flight Attendant and while I worked for two American companies, I also lived in the U.K. for 6 years.
Double seat belts or "belly belts" are banned by U.S., Canadian and German companies (perhaps others) because they are dangerous for the child. In forward impact, the adult would crush the child. I used to take the parents shoulder and gently show them the action that would cause. This was especially effective if there was a language barrier. Needless to say, this quickly convinced them that it was safer to have their child loose in their laps!
The CAA as well as some other foreign airline insist on them because they claim that they'll take the risk with the child to prevent a flying object in the cabin. The EU has discussed banning these devices but unfortunately, this issue was confused with requiring a car seat. As most of us know, that wont happen anywhere, anytime soon! So the "belly belts" continue to be used. In fact, Germany only got wise to this issue a few years ago and brought in the ban.
The truth is that a car seat is really the only way to fly safely with a child. There are no real alternatives. "Lap babies" continue to be allowed for commercial reasons and quite frankly, air travel itself is so safe that there is little chance of anything going wrong. Your child is safer doing flip-flops down the aisle on an airplane than he or she was on the ride to the airport in a car seat.
Which gets down to my final point, accidents are rare enough that there are no real statistics for the airlines to break down. The airlines usually don't release all information regarding accidents to the public for a number of reasons. The FAA uses car crash data to make these decisions (since take-off and landing are similar to high speed car dynamics). The few cases where a parent has spoken up, the details have be argued. If anyone is interested, the Sioux City accident is often cited where there were quite a few lap babies...and that occurred 20 years ago!
On U.S. airlines especially, be sure that the child is not strapped in with your as we were told specifically to look for this and could get your crew in trouble if there is a FAA inspector on board. For more information on using a car seat, see the car seat thread.
So while it's technically better to have your baby loose in your lap, if you find yourself on an airline that still uses belly belts, remember that when you buy a ticket, you are agreeing to that airlines' rules. When buying, some parents specifically try to book on airlines where they are not required. Please don't concern yourself with this issue too much and cooperate with the crew. Your child's safety is in the fact your are on a commercial aircraft and the chances of any incident are slim.