Thanks all for your input - there is something here to support every point of view: from those of you who are caravanners, to those of you whose are anti-caravan, to those responding to my request for suggestions of a car that is reliable, economical, petrol and no bigger than a Civic with the suggestion of getting a Discovery :-) Incidentally I don't want diesel because I've had several - I don't feel comfortable with the particulates coming out of them, and I don't feel comfortable potentially not being able to drive into city centres if needed (although as a true CC'er I cycle into my own city centre as a rule)
I think the main issue I have with the Civic is that it's torque is so minimal, and quite high up the rev range comapred to previous cars (mainly diesels) and there is still a little part of my brain that tells me that if it sounds like the engine is revving hard I should change gear. Maybe it's youthful memories of the 4 speed 'box on my Viva. I've had a bit of a play with the default weight settings at towcar.info though based on the replies saying that it should be more than powerful enough, and actually if you set realistic loads (i.e. there is more than the default of 200kg in the car including the passengers) it looks like it might work out ok. I set it to 300kg in the car (three people, clothes and as much of the awning as will fit - basically I'd try and get all the heavy stuff in the car) and 200kg in the caravan (awning poles, three bikes, deckchairs, boules etc) and then the balance looks ok. They say (translated from Dutch) "The Honda Civic - 1.8i-Vtec with a Caravan as an example with an actual weight of 1200 kg is in general a good match and suitable for all journeys on all kinds of roads."
As mentioned, I just need to find a caravan that is light enough - around 1100kg max.
I passed my test when Global Hypercolor was considered the height of fashion so I'm not required to have additional training, and I've towed a trailer. But maybe some training would be in order, although I'm not sure what training would help overcome a gust of wind that can tip a properly loaded caravan attached to a big old 4x4!