Hi Chrissylizzie
Confusing isn't it!
There are a number of different issues here. Firstly are UK caravans strong enough to carry a rear mounted bike rack, I don't know, but asking the dealer or manufacture should illicit an answer. A manufacture that provides additional strengthening for such racks will be prepared to tell you, so if they don't tell you the assume the caravan may not be strong enough.
Do bike racks cause instability? You mention the pendulum effect, and yes it will exacerbate the effect, but for some outfits it may still be easily within its controllable limits, where as for others it may be too much. There is no simple way to accurately predict the size of the effect on any outfit, except to say that if an outfit is already difficult to control, it will be more difficult with a loaded bike rack.
The length of an A frame does have an appreciable effect on the controllability of a trailer. The longer the A frame the lower are the forces the tow hitch and so the tow car can maintain better control of the trailer. So continental caravans with longer A frames will seem easier to control when towing. But also they often have dampers fitted to the suspension, which also aids stability.
Do not forget that the bike rack will extend the length of the caravan. It is essential that the number plate must not be obscured, and that the rear road lights should be
at the extremity of the outfit. A new number plate and lights board may be necessary. It is also advisable to clearly mark any protrusions such as peddles so that drivers behind can easily see the rear of your outfit.
The additional length of the caravan and bike rack may be problem when reversing but should make little difference when forward towing.
I cannot give a definitive answer to this but I hope I have given some food for thought.