I think it would cause problems because the radius of the wheel arch is designed to accept the wheel specified by the manufacturer plus if you have a spare wheel carrier in the front locker or underneath then the larger wheel and tyre may not fit. A larger diameter wheel and tyre would effectively look quite odd but even if you did happen to do this then you may find it difficult to obtain insurance as it would be deemed as a modification.
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You need to fit caravan specific alloys. If you did find random secondhand car alloys of correct PCD & offset the load rating of wheels may be insufficient. To retain same overall diameter as 13inch wheel, a 15inch would have to be fitted with lower profile tyres which again may not be available in sufficient load rating. To fit different wheels/tyres you need indepth knowledge of what you are trying to attempt or you risk disaster.