Our 1.2 Jazz can tow 450kg unbraked or 1000kg braked (although I wouldn't fancy trying to pull 1000kg up any sort of hill with it). 1.4 models seem to have the same limits.
I have towed a camping trailer with my old 53plate Honda Jazz 1.4 Sport afew years ago, but l have no knowledge of the weight of your Suncamp so cannot really comment without that. The Jazz was a fairly good towcar for basic camping needs, and we handed it over to our daughter when we upgraded to a 1.8 Civic when we bought a Caravan, and its still going strong in its 10th year.
Our camping trailer was unbreaked and weighed about 450kg laden, the car mainly had 2 adults and 2 teenagers in it whilst towing, plus a boot full of luggage and their gear. It happily cruised on the motorway at 50mph, but did need a bit of gearwork when it came to inclines and strong headwinds.
Julia
------------- Just love to be out amoungst Nature and Wildlife
Celebrating 37 years of Caravanning in 2019, Recently Considered Retiring, but Totally Addicted for Life!
We've towed our Dandy Designer (500kg) with a Jazz 1.4 no problems except up very steep hills were she was a little slow. So depending on the weight of your TT I would have thought you should be fine.
The sunncamp 350se is 375kg unladen and 500kg gross. Just check on the towbar website to find the limits of your jazz. The 1.4 is a fairly torquey lump so should be ok but double check the weight limit to stay legal.
------------- Stupidity is natures way of thinning the numbers
According to autotrader specs the jazz can pull 450kg max so ok if yours is a mk1 jazz as in the one I've just checked. Doesn't leave you a lot of weight to put in the trailer though.
------------- Stupidity is natures way of thinning the numbers